Aging and temperature changes in the passive components of an LCL-filter grid connected converter system (GCCs) may lead to parameter uncertainties, which can in turn influence its modeling accuracy for finite-control-set model predictive control (FCS-MPC). The presence of model errors will change the resonance point and deteriorate the power quality of the grid current, in turn degrading the active damping performance. In this situation, there is a serious possibility that the GCCs may malfunction and automatically disconnect from the grid, causing great challenges to the system stability. To solve this problem, first, prediction error analysis in FCS-MPC due to the model parameter errors is presented. Second, to achieve high accuracy and fast filter parameter estimation in utility, an adaptive online parameter identification method based on gradient descent optimization (GDO) has been proposed. Finally, to further reduce the searching time needed by the optimal iteration step, a variable iteration step searching method based on the root-mean-square-prop (RM-Sprop) GDO method is proposed. Experimental studies of an LCL-GCCs prototype in the laboratory have been conducted to validate the effectiveness of the proposed method.