This brief introduces the Inverse-free hybrid spatial-temporal derivative neural network (IHSTDNN), a novel neural network that integrates principles from gradient neural networks (GNN) and zeroing neural networks (ZNN) to address the time-varying matrix Moore-Penrose inverse. The IHSTDNN features an explicit dynamic structure, eliminating the need for inverse operations. The design of its circuit is outlined, and the model’s convergence and robustness are examined theoretically. Numerical simulations and experimental data demonstrate that the IHSTDNN outperforms other existing models, achieving a faster convergence rate and reduced steady-state error.