This paper proposes an L_p (0<p<1) quasi norm state estimator for power system static state estimation. Compared with the existing L₁ and L₂ norm estimators, the proposed estimator can suppress the bad data more effectively. The robustness of the proposed estimator is discussed, and an analysis shows that its ability to suppress bad data increases as p decreases. Moreover, an algorithm is suggested to solve the non-convex state estimation problem. By introducing a relaxation factor in the mathematical model of the proposed estimator, the algorithm can prevent the solution from converging to a local optimum as much as possible. Finally, simulations on a 3-bus DC system, the IEEE 14-bus and IEEE 300-bus systems as well as a 1204-bus provincial system verify the high computation efficiency and robustness of the proposed estimator.