This paper proposes a directed complex dynamical network consisting of N linearly and diffusively coupled identical reaction-diffusion neural networks. Based on the Lyapunov functional method and the pinning control technique, some sufficient conditions are obtained to guarantee the synchronization of the proposed network model. In addition, an adaptive strategy is proposed to obtain appropriate coupling strength for achieving network synchronization. Furthermore, the pinning adaptive synchronization problem is also investigated in this paper, and a general criterion for ensuring network synchronization is established. Finally, a numerical example is provided to illustrate the effectiveness of the proposed criteria.