Smart Grid State Estimation (SE) aims at providing robust and accurate system state estimate for subsequent control operations to accommodate the disturbance of highly intermittent components. Conventional SE for AC Power Grid formulates the estimation process as a non-convex optimization problem, which may reach a local optimal and stop. To compensate the drawback, Semidefinite Programming (SDP) was recently applied to convexify the non-convex problem with rank one relaxation technique, which shows perspectives with approximately globally optimal estimate. However, as the SDP approach is essentially a centralized algorithm, it is computationally expensive and non-robust to partial network failure, bad data. etc. To ameliorate the current SDP SE approach, this paper presents a distributed algorithm by employing Lagrangian method and graph theory results and particularly by dividing power networks in accordance with network 'cliques'. Correspondingly, significant improvements are illustrated in simulations on IEEE test beds.