Even with modern smart metering systems, erroneous measurements of the real and reactive power in the power system are unavoidable. Multiple erroneous parameters and measurements may occur simultaneously in the state estimation of a bulk power system. This paper proposes a gross error reduction index (GERI)-based method as an additional module for existing state estimators in order to identify multiple erroneous parameters and measurements simultaneously. The measurements are acquired from a supervisory control and data acquisition system and mainly include voltage amplitudes, branch current amplitudes, active power flow, and reactive power flow. This method uses a structure consisting of nested two loops. First, gross errors and the GERI indexes are calculated in the inner loop. Second, the GERI indexes are compared and the maximum GERI in each inner loop is associated with the most suspicious parameter or measurement. Third, when the maximum GERI is less than a given threshold in the outer loop, its corresponding erroneous parameter or measurement is identified. Multiple measurement scans are also adopted in order to increase the redundancy of measurements and the observability of parameters. It should be noted that the proposed algorithm can be directly integrated into the Weighted Least Square estimator. Furthermore, using a faster simplified calculation technique with Givens rotations reduces the required computer memory and increases the computation speed. This method has been demonstrated in the IEEE 14-bus test system and several matpower cases. Due to its outstanding practical performance, it is now used at six provincial power control centers in the Eastern Grid of China.