Compared to the linear activation function, a suitable nonlinear activation function can accelerate the convergence speed. Based on this finding, we propose two modified Zhang neural network (ZNN) models using different nonlinear activation functions to tackle the complex-valued systems of linear equation (CVSLE) problems in this paper. To fulfill this goal, we first propose a novel neural network called NRNN-SBP model by introducing the sign-bi-power activation function. Then, we propose another novel neural network called NRNN-IRN model by introducing the tunable activation function. Finally, simulative results demonstrate that the convergence speed of NRNN-SBP and the NRNN-IRN is faster than that of the FTRNN model. On the other hand, these results also reveal that different nonlinear activation function will have a different effect on the convergence rate for different CVSLE problems