The presence of gross errors in the process data for the power system state estimation (PSSE) algorithm is very crucial as they may severely degrade its results. The conventionally used state estimator is based on the method of the weighted least squares (WLS) which is not robust against the bad measurements that results in larger deviation in output estimates. In this study, a new robust algorithm based on the quasi weighted least squares (QWLS) estimator is presented. The robustness of the QWLS approach is achieved by reducing the impact of bad measurements on the objective function. In the existence of gross errors, the proposed algorithm provides estimates as good as those that are achieved by the conventional method of the WLS when no gross error exists in the process data. The implementation of the proposed algorithm has been illustrated for the case studies on the 6-bus and IEEE 14-bus power networks. The numerical results validate the performance of the proposed estimator in the PSSE algorithm. © 2016 Author(s).