I know that this thread is quite old, but I had this problem and I came up with a cool solution which can be very useful to many because it corrects/extended the Volley library on many aspects.
I spotted some not supported-out-of-box Volley features:
- This 
JSONObjectRequest is not perfect: you have to expect a JSON at the end (see the Response.Listener<JSONObject>). 
- What about Empty Responses (just with a 200 status)?
 
- What do I do if I want directly my POJO from the 
ResponseListener? 
I more or less compiled a lot of solutions in a big generic class in order to have a solution for all the problem I quoted.
  /**
  * Created by laurentmeyer on 25/07/15.
  */
 public class GenericRequest<T> extends JsonRequest<T> {
     private final Gson gson = new Gson();
     private final Class<T> clazz;
     private final Map<String, String> headers;
     // Used for request which do not return anything from the server
     private boolean muteRequest = false;
     /**
      * Basically, this is the constructor which is called by the others.
      * It allows you to send an object of type A to the server and expect a JSON representing a object of type B.
      * The problem with the #JsonObjectRequest is that you expect a JSON at the end.
      * We can do better than that, we can directly receive our POJO.
      * That's what this class does.
      *
      * @param method:        HTTP Method
      * @param classtype:     Classtype to parse the JSON coming from the server
      * @param url:           url to be called
      * @param requestBody:   The body being sent
      * @param listener:      Listener of the request
      * @param errorListener: Error handler of the request
      * @param headers:       Added headers
      */
     private GenericRequest(int method, Class<T> classtype, String url, String requestBody,
                           Response.Listener<T> listener, Response.ErrorListener errorListener, Map<String, String> headers) {
         super(method, url, requestBody, listener,
                 errorListener);
         clazz = classtype;
         this.headers = headers;
         configureRequest();
     }
     /**
      * Method to be called if you want to send some objects to your server via body in JSON of the request (with headers and not muted)
      *
      * @param method:        HTTP Method
      * @param url:           URL to be called
      * @param classtype:     Classtype to parse the JSON returned from the server
      * @param toBeSent:      Object which will be transformed in JSON via Gson and sent to the server
      * @param listener:      Listener of the request
      * @param errorListener: Error handler of the request
      * @param headers:       Added headers
      */
     public GenericRequest(int method, String url, Class<T> classtype, Object toBeSent,
                           Response.Listener<T> listener, Response.ErrorListener errorListener, Map<String, String> headers) {
         this(method, classtype, url, new Gson().toJson(toBeSent), listener,
                 errorListener, headers);
     }
     /**
      * Method to be called if you want to send some objects to your server via body in JSON of the request (without header and not muted)
      *
      * @param method:        HTTP Method
      * @param url:           URL to be called
      * @param classtype:     Classtype to parse the JSON returned from the server
      * @param toBeSent:      Object which will be transformed in JSON via Gson and sent to the server
      * @param listener:      Listener of the request
      * @param errorListener: Error handler of the request
      */
     public GenericRequest(int method, String url, Class<T> classtype, Object toBeSent,
                           Response.Listener<T> listener, Response.ErrorListener errorListener) {
         this(method, classtype, url, new Gson().toJson(toBeSent), listener,
                 errorListener, new HashMap<String, String>());
     }
     /**
      * Method to be called if you want to send something to the server but not with a JSON, just with a defined String (without header and not muted)
      *
      * @param method:        HTTP Method
      * @param url:           URL to be called
      * @param classtype:     Classtype to parse the JSON returned from the server
      * @param requestBody:   String to be sent to the server
      * @param listener:      Listener of the request
      * @param errorListener: Error handler of the request
      */
     public GenericRequest(int method, String url, Class<T> classtype, String requestBody,
                           Response.Listener<T> listener, Response.ErrorListener errorListener) {
         this(method, classtype, url, requestBody, listener,
                 errorListener, new HashMap<String, String>());
     }
     /**
      * Method to be called if you want to GET something from the server and receive the POJO directly after the call (no JSON). (Without header)
      *
      * @param url:           URL to be called
      * @param classtype:     Classtype to parse the JSON returned from the server
      * @param listener:      Listener of the request
      * @param errorListener: Error handler of the request
      */
     public GenericRequest(String url, Class<T> classtype, Response.Listener<T> listener, Response.ErrorListener errorListener) {
         this(Request.Method.GET, url, classtype, "", listener, errorListener);
     }
     /**
      * Method to be called if you want to GET something from the server and receive the POJO directly after the call (no JSON). (With headers)
      *
      * @param url:           URL to be called
      * @param classtype:     Classtype to parse the JSON returned from the server
      * @param listener:      Listener of the request
      * @param errorListener: Error handler of the request
      * @param headers:       Added headers
      */
     public GenericRequest(String url, Class<T> classtype, Response.Listener<T> listener, Response.ErrorListener errorListener, Map<String, String> headers) {
         this(Request.Method.GET, classtype, url, "", listener, errorListener, headers);
     }
     /**
      * Method to be called if you want to send some objects to your server via body in JSON of the request (with headers and muted)
      *
      * @param method:        HTTP Method
      * @param url:           URL to be called
      * @param classtype:     Classtype to parse the JSON returned from the server
      * @param toBeSent:      Object which will be transformed in JSON via Gson and sent to the server
      * @param listener:      Listener of the request
      * @param errorListener: Error handler of the request
      * @param headers:       Added headers
      * @param mute:          Muted (put it to true, to make sense)
      */
     public GenericRequest(int method, String url, Class<T> classtype, Object toBeSent,
                           Response.Listener<T> listener, Response.ErrorListener errorListener, Map<String, String> headers, boolean mute) {
         this(method, classtype, url, new Gson().toJson(toBeSent), listener,
                 errorListener, headers);
         this.muteRequest = mute;
     }
     /**
      * Method to be called if you want to send some objects to your server via body in JSON of the request (without header and muted)
      *
      * @param method:        HTTP Method
      * @param url:           URL to be called
      * @param classtype:     Classtype to parse the JSON returned from the server
      * @param toBeSent:      Object which will be transformed in JSON via Gson and sent to the server
      * @param listener:      Listener of the request
      * @param errorListener: Error handler of the request
      * @param mute:          Muted (put it to true, to make sense)
      */
     public GenericRequest(int method, String url, Class<T> classtype, Object toBeSent,
                           Response.Listener<T> listener, Response.ErrorListener errorListener, boolean mute) {
         this(method, classtype, url, new Gson().toJson(toBeSent), listener,
                 errorListener, new HashMap<String, String>());
         this.muteRequest = mute;
     }
     /**
      * Method to be called if you want to send something to the server but not with a JSON, just with a defined String (without header and not muted)
      *
      * @param method:        HTTP Method
      * @param url:           URL to be called
      * @param classtype:     Classtype to parse the JSON returned from the server
      * @param requestBody:   String to be sent to the server
      * @param listener:      Listener of the request
      * @param errorListener: Error handler of the request
      * @param mute:          Muted (put it to true, to make sense)
      */
     public GenericRequest(int method, String url, Class<T> classtype, String requestBody,
                           Response.Listener<T> listener, Response.ErrorListener errorListener, boolean mute) {
         this(method, classtype, url, requestBody, listener,
                 errorListener, new HashMap<String, String>());
         this.muteRequest = mute;
     }
     @Override
     protected Response<T> parseNetworkResponse(NetworkResponse response) {
         // The magic of the mute request happens here
         if (muteRequest) {
             if (response.statusCode >= 200 && response.statusCode <= 299) {
                 // If the status is correct, we return a success but with a null object, because the server didn't return anything
                 return Response.success(null, HttpHeaderParser.parseCacheHeaders(response));
             }
         } else {
             try {
                 // If it's not muted; we just need to create our POJO from the returned JSON and handle correctly the errors
                 String json = new String(response.data, HttpHeaderParser.parseCharset(response.headers));
                 T parsedObject = gson.fromJson(json, clazz);
                 return Response.success(parsedObject, HttpHeaderParser.parseCacheHeaders(response));
             } catch (UnsupportedEncodingException e) {
                 return Response.error(new ParseError(e));
             } catch (JsonSyntaxException e) {
                 return Response.error(new ParseError(e));
             }
         }
         return null;
     }
     @Override
     public Map<String, String> getHeaders() throws AuthFailureError {
         return headers != null ? headers : super.getHeaders();
     }
     private void configureRequest() {
         // Set retry policy
         // Add headers, for auth for example
         // ...
     }
 }
It could seem a bit overkill but it's pretty cool to have all these constructors because you have all the cases:
(The main constructor wasn't meant to be used directly although it's, of course, possible).
- Request with response parsed to POJO / Headers manually set / POJO to Send
 
- Request with response parsed to POJO / POJO to Send
 
- Request with response parsed to POJO / String to Send
 
- Request with response parsed to POJO (GET)
 
- Request with response parsed to POJO (GET) / Headers manually set
 
- Request with no response (200 - Empty Body) / Headers manually set / POJO to Send
 
- Request with no response (200 - Empty Body) / POJO to Send
 
- Request with no response (200 - Empty Body) / String to Send
 
Of course, in order that it works, you have to have Google's GSON Lib; just add:
compile 'com.google.code.gson:gson:x.y.z'
to your dependencies (current version is 2.3.1).