This paper considers the finite-time synchronization problem of stochastic complex networks with mixed delays. A controller based on adaptive aperiodic intermittent control strategy is constructed, which can guarantee that network systems with unknown characteristics of the controlled object or a wide range of disturbance characteristics achieve synchronization in the finite-time. Moreover, relying on various inequality techniques, the finitetime synchronization criterion is obtained by establishing the Lyapunov function. Then, the synchronization of the stochastic network system can still be achieved, when the stochastic disturbance does not exist. Finally, the rationality of the theoretical results is tested by an example of Chua’s circuit system.