Abstract In this paper, we investigate a new model of complex networks with continuous dynamics and Boolean mechanism. Firstly, we give the expression of this new class of complex networks. Next, based on semi-tensor product technique and Lyapunov function, a criterion of globally exponential synchronization for the complex networks is given. Further, we take impulsive effects into consideration and establish corresponding conditions of globally exponential synchronization. Finally, examples are simulated to illustrate the effectiveness of the main obtained results.