A smart grid is a complex system using power transmission and distribution networks to connect electric power generators to consumers across a large geographical area. Due to their heavy dependencies on information and communication technologies, smart grid applications, such as state estimation, are vulnerable to various cyber-attacks. False data injection attacks (FDIA), considered as the most severe threats for state estimation, can bypass conventional bad data detection mechanisms and render a significant threat to smart grids. In this paper, we propose a novel FDIA detection mechanism based on a wide and recurrent neural networks (RNN) model to address the above concerns. Simulations over IEEE 39-bus system indicate that the proposed mechanism can achieve a satisfactory FDIA detection accuracy.