A wide area measurement system (WAMS) is a technology developed to improve the stability of the power system in the past few decades, which provides a distributed control structure of a highly interconnected power system. However, the critical issues of security in WAMSs are rising to a new class of control problems due to the malicious attacks. This work studies the distributed model predictive control (DMPC) problem for wide area measurement power systems under malicious attacks. The malicious attacks model as time-varying data injection attacks which describe delayed input states. The traditional three-order model of an interconnection power system is modified to a distributed model with coupling control inputs. A sufficient condition to ensure that the closed loop system with asymptotic stability is obtained by using Lyapunov theorem and linear matrix inequality technology. An iterative DMPC algorithm is proposed to design the distributed controllers based on a cooperative control strategy. Finally, a simulation example of a three-machine nine-node power system is presented to verify the effectiveness of the proposed algorithm.