Smart grids are essentially electric grids that use information and communication technology to provide reliable, efficient electricity transmission and distribution. Security and trust are of paramount importance. Among various emerging security issues, FDI attacks are one of the most substantial ones, which can significantly increase the cost of the energy distribution process. However, most current research focuses on countermeasures to FDIs for traditional power grids rather smart grid infrastructures. We propose an efficient and real-time scheme to detect FDI attacks in smart grids by exploiting spatial-temporal correlations between grid components. Through realistic simulations based on the US smart grid, we demonstrate that the proposed scheme provides an accurate and reliable solution.