Application of computing and communications intelligence effectively improves the quality of monitoring and control of smart grids. However, the dependence on information technology also increases vulnerability to malicious attacks. False data injection (FDI), that attack on the integrity of data, is emerging as a severe threat to the supervisory control and data acquisition system. In this paper, we exploit deep learning techniques to recognize the behavior features of FDI attacks with the historical measurement data and employ the captured features to detect the FDI attacks in real-time. By doing so, our proposed detection mechanism effectively relaxes the assumptions on the potential attack scenarios and achieves high accuracy. Furthermore, we propose an optimization model to characterize the behavior of one type of FDI attack that compromises the limited number of state measurements of the power system for electricity theft. We illustrate the performance of the proposed strategy through the simulation by using IEEE 118-bus test system. We also evaluate the scalability of our proposed detection mechanism by using IEEE 300-bus test system.