Smart grid is built by combination of electric and information technologies and achieves the two-way interaction between power utilization and power generation. Unfortunately, new security threats appears together with cyber-physical communication systems. In order to properly monitor power network, an effective cyber attack detection and state estimation method are required to know attack and system states. This article considers the problem of robust grid state estimation and suggests a technique for distributed state estimation in power networks. First, the distribution power system incorporating multiple synchronous generators is modeled as a state-space framework, where attack occurs in measurements. Basically, the false data injection attacks can interfere with state estimation process by tampering with sensor measurements. Using mean squared error principle, the distributed dynamic state estimation algorithm is designed where local and neighboring gains are obtained using optimal filter and graph theory. For local gain computation, the attack parameter is obtained using the Bayesian learning process. The convergence condition of the proposed approach is derived. Extensive simulation results show that the proposed approach is able to estimate the system state within a short period of time. Hopefully, the proposed methodology can be used to tolerate the cyber attacks for improving the confidence of the grid state estimation process.