Complex-valued time-varying Sylvester equation (CVTVSE) has been successfully applied into mathematics and control domain. However, the computation load of solving CVTVSE will rise significantly with the increase of sampling rate, and it is a challenging job to tackle the CVTVSE online. In this paper, a new sign-multi-power activation function is designed. Based on this new activation function, an improved complex-valued Zhang neural network (ICZNN) model for tackling the CVTVSE is established. Furthermore, the strict proof for the maximum time of global convergence of the ICZNN is given in detail. A total of two numerical experiments are employed to verify the performance of the proposed ICZNN model, and the results show that, as compared with the previous Zhang neural network (ZNN) models with different nonlinear activation functions, this ICZNN model with the sign-multi-power activation function has a faster convergence speed to tackle the CVTVSE.