In order to solve the time-varying complex Sylvester equation, the finite-time complex-valued zeroing neural network (FTCVZNN) model is proposed in this study, and its global and asymptotic convergences are studied. The asymptotic stability analysis is investigated with either a general activation function that satisfies a condition or with an odd monotonically increasing activation function. To examine the proposed approach, an application of the inverted pendulum on a cart system is considered. The upper bound time on convergence for the FTCVZNN model is also given. Some simulations are given, and the results demonstrate the effectiveness and performance of the suggested methodology in comparison to the baseline methods.