This paper proposes a new zeroing neural network (NZNN) for solving the dynamic complex value linear equation (DCVLE). To achieve a faster convergence rate and improve the feasibility of the ZNN model, a bounded nonlinear mapping function is designed that endowed the NZNN model with finite-time convergence. Furthermore, regarding the different forms of the DCVLE in the Cartesian complex plane and the polar complex plane, two distinct NZNN models are proposed. In addition, the global convergence and the finite-time convergence of the NZNN models are analyzed and demonstrated by numerical simulations. Lastly, the NZNN model is successfully applied to the acoustic location and the control of a robotic manipulator, which well demonstrates its feasibility and efficiency.