Smart grid is a complex cyber–physical system formed by integrating the physical power system with the sensing, computing technology, and communication systems. Security risks of cyber attacks increase due to the deep reliance on a wide area communication network. One of the dangerous cyber attacks against smart grids is False Data Injection Attack (FDIA), which can cause economic and physical damage. Almost all FDIAs target a module called state estimation due to the key role it plays in monitoring and control of smart grids. Although many methods have been proposed for robust state estimation against FDIAs, they are not robust to all types of FDIAs such as cyber topology attacks or have computational complexity. This thesis develops a real-time robust state forecasting method against cyber attacks. Simulations performed on IEEE systems demonstrate the effectiveness of the proposed method in increasing the accuracy of state forecasting and cyber attack detection.