In this paper,the asymptotical mean-square stability analysis problem is considered for a class of cellular neural networks(CNNs)with random delay.Compared with the previous work,the delay is modeled by a continuous-time homogeneous Markov process with a finite number of states.The main purpose of this paper is to establish easily verifiable conditions under which the random delayed cellular neural network is asymptotic mean-square stability.By using some stochastic analysis techniques and Lyapunov-Krasovskii functional,some conditions are derived to ensure that the cellular neural networks with random delay is asymptotical meansquare stability.A numerical example is exploited to show the vadlidness of the established results.