Abstract: In this paper, the synchronization problem of a class of nonlinear coupled neural networks with Markovian jump and variable delay is discussed. The coupling strength of the model is a random variable, the coupling structure of the network switches dynamically according to a continuous time Markov chain, and the influence of nonlinear coupling term and time-varying delay is considered. By constructing a suitable Lyapunov function and using the linear matrix inequality method, the sufficient conditions for the global mean square asymptotic synchronization of the network model are obtained. Finally, a numerical example is given to demonstrate the effectiveness of the theoretical results.