This paper is concerned with the quasi-synchronization issue of linearly coupled networks with discontinuous nonlinear functions in each isolated node. Under the framework of Filippov systems, the existence and boundedness of solutions for such complex networks can be guaranteed by the matrix measure approach. A design method is presented for the synchronization controllers of coupled networks with non-identical discontinuous systems. Moreover, a sufficient condition is derived to ensure the quasi-synchronization of switched coupled complex networks with discontinuous isolated nodes, which could be controlled by some designed linear controllers. The obtained results extend the previous work on the synchronization issue of coupled complex networks with Lipschitz continuous conditions. Numerical simulations on the coupled chaotic systems are given to demonstrate the effectiveness of the theoretical results.