You need to add a zero to your variable at the end.
.data
szSrc db "Your string", 0
If you need to do it at runtime, you need to get the length of your variable (szSrc), and then you could write something like this:
lea eax, szSrc
mov byte ptr [eax+szSrcLen], 0
Note : it is important to provide a valid length. If you don't know the correct string length then it will be impossible to make a null string.