During the process of the general practical applications and scientific researches, time varying issues are an inescapable challenge to be tackled. In this article, a pre-defined finite-time zeroing neural networks (PDFT-ZNN) is devoted to solve the linear time-variant matrix equation (TVME) E (t) X (t) G (t) = D (t) within a finite time (FT), which contrasts with the general ZNN (G-ZNN) models with relatively long global convergence time. Moreover, the proposed PDFT-ZNN model's convergence time could be calculated in advance by adhering to the designed system parameters; this has nothing to do with the model's initial state. Additionally, after the convergence analysis, if the solution error is relative small, the simple and effective method is to introduce a linear item to accelerate the convergence speed, in comparison with only the power-type ZNN models. Theory-based analysis and simulation-based results further validate that, the neural state solved by the presented FT-ZNN model can reach the theory-based solution of E (t) X (t) G (t) = D (t) within the pre-defined finite time. • Th presented PDFT-ZNN model can predict the convergence time for the control system in advance. • A detailed theoretical analysis are carried out for the proposed PDFT-ZNN model. • The illustrative example is computed and examined for the proposed PDFT-ZNN model. [ABSTRACT FROM AUTHOR]