Different from the traditional linearly activated gradient-based neural network model (GNN model), two nonlinear activation functions are presented and investigated to construct two nonlinear gradient-based neural network models (NGNN-1 model and NGNN-2 model) for matrix inversion in this paper. For comparative and illustrative purposes, the traditional GNN model is also used to solve matrix inversion problems under the same circumstance. In addition, the simulation results of the computer finally confirm the validity and superiority of the two nonlinear gradient-based neural network models specially activated by two nonlinear activation functions for matrix inversion, as compared with the traditional GNN model