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The evolution of traditional energy networks toward smart grids increases security vulnerabilities in the power system infrastructure. State estimation plays an essential role in the efficient and reliable operation of power systems, so its security is a major concern. Coordinated cyber-attacks, including false data injection (FDI) attack, can manipulate smart meters to present serious threats to grid operations. In this paper, a robust state estimation algorithm against FDI attack is presented. As a solution to mitigate such an attack, a new analytical technique is proposed based on the Markov chain theory and Euclidean distance metric. Using historical data of a set of trusted buses, a Markov chain model of the system normal operation is formulated. The estimated states are analyzed by calculating the Euclidean distance from the Markov model. States, which match the lower probability, are considered as attacked states. It is shown that the proposed method is able to detect malicious attack, which is undetectable by traditional bad data detection (BDD) methods. The proposed robust dynamic state estimation algorithm is built on a Kalman filter, and implemented on the massively parallel architecture of graphic processing unit using fine-grained parallel programming techniques. Numerical simulations demonstrate the efficiency and accuracy of the proposed mechanism.