This article investigates finite-time synchronization (FTS) of network systems (NSs) with intermittent delayed couplings and stochastic perturbations. A channel matrix is introduced to describe the partial couplings of NSs, and state-dependent parameters are also considered to characterize the weight matrices. In order to deal with the intermittent couplings and reduce the control cost, an intermittent control scheme is designed. Based on the 2-norm Lyapunov function and new analytical methods, FTS is achieved, and the settling time is also estimated. Besides, two special cases are presented which indicate that our models are more general than some existing models. Finally, the synchronization criteria are verified by some simulations.