First of all, don't use str as a variable name, it will mask the built-in name.
As for counting characters in a string, just use the str.count() method:
>>> s = "Green tree"
>>> s.count("e")
4
If you are just interested in understanding why your current code doesn't work, you are printing 1 four times because you will find four occurrences of 'e', and when an occurrence is found you are printing len(scr) which is always 1.
Instead of printing len(scr) in your if block, you should be incrementing a counter that keeps track of the total number of occurrences found, it looks like you set up a variable a that you aren't using, so the smallest change to your code to get it to work would be the following (however as noted above, str.count() is a better approach):
str= "Green tree"
scr= "e"
cstr= len(str)
n=0
a=0
while n < cstr:
    if str[n] == scr:
        a+=1
    n=n+1
print(a)