I tried to draw Moore FSM that accept sequence 111101 but I'm not sure if it is right
here is my solution

 

What is meant by non-overlapping? I'm sure if you ask three different people you'd get three slightly different answers. Your answer will affect the way your state diagram should look...

Two things I see are:

1. The last state, S6, has no definition for what happens when in that state and the input is 1.
2. What is being stated in the lower half of the state? In a Moore machine, it is the output value, are you stating that Z=x, where x is the output value? It looks like it could be 20 and 21. You should explain your system before you ask if it is correct.

 

A couple other things to note:

Assuming that Z0 means to output a '0' and Z1 means to output a '1', then why do you have z1 as the output condition for S5?

Leaving S5 you have two arrows, both of which are labeled '1'. Does that make sense?