Abstract: In nature and engineering problems, successive lag synchronization is an important synchronization phenomenon. Control theory has good economic and practical value, especially the intermittent control theory. In addition, the influence of noise has never been considered in previous studies on successive lag synchronization. Therefore, it is necessary to study the successive lag synchronization of complex dynamic networks with noise by using intermittent control. In order to obtain the synchronization conditions of the model, firstly, a distributed linear coupling complex dynamic network model with noise disturbance was established. Secondly, an intermittent control was designed to ensure that the control signal is not activated in the whole interval, but only in the control subinterval, thus to make the controlled network reach the desired state. Based on the controlled network, a sufficient condition was derived analytically to ensure the mean square stability of successive lay synchronization. Finally, the intermittent control strategy was applied to Chua's circuit and other practical systems to test the accuracy of the theoretical results.Numerical simulation results verify the correctness and validity of the theoretical results.