This paper presents an efficient method to identify and estimate of branch parameter (series and shunt admittances) errors in power system state estimation. The proposed method is composed of three stages. In the stage 1, the modified weighted least square state estimation is solved and the normalized Lagrange multipliers for branch parameter errors are computed. In the stage 2, the errors in branch parameter are identified based on the results of the stage 1. In the stage 3, erroneous branch parameter values can be estimated using a proposed linear approximation approach by eliminating the necessity to augmented state vector. Important advantage of the proposed method is that there is no need to specify and suspect set of parameters, a priori that it is necessary in other recently published methods. Finally, the validity and performance of the proposed procedure is evaluated based on the simulation results of the IEEE-30 and 57 bus test systems and these results are compared with other recently published methods