This paper is concerned with p-th moment exponential stability of fuzzy cellular neural networks(FCNNs) with time-varying delays and stochastic effects. Constructing some suitable Lyapunov functional and using stochastic analysis technique, some sufficient conditions are presented to guarantee p-th moment exponential stability of stochastic FCNNs with time-varying delays. The condition contains and improves some of the previous results in the earlier references. Moreover an example is provided to illustrate results obtained.