State estimation of power system is the basis of all the high level application and analysis for dispatch centers. Against the bad convergence of the WLAV (weighted least absolute value)-based state estimation method, a new robust state estimation method based on exponential weight function (E-LAV) is presented in the paper. This method uses an exponential weight function to replace discontinues weight function of WLAV to improve the poor convergence. The results of the sample system of 4-node system and the IEEE 118-node system show that the E-LAV-based state estimation method not only owns the similar convergence as WLS-based method, and also owns a strong robustness. Through modifying the weight matrix of the least squares, the proposed new method has good prospects for application in practical engineering.