Time-varying linear equations (TVLEs) are encountered frequently in artificial intelligence and robotics. Therefore, solving TVLEs efficiently and accurately is important for engineering applications. Recurrent neural networks (RNNs), including gradient-dynamics based neurodynamic networks (GDNNs), can solve such equations but inevitably generate errors during the iteration process. Getz-Marsden dynamic inverters (GMDIs) and error-dynamics based neurodynamic networks (EDNNs), while eliminating these errors, involve matrix inversion and information about the time derivatives of the coefficients, thus increasing the computational cost. To address these issues, a gated recurrent unit (GRU) model-enhanced GDNN (GRU-GDNN) is proposed in this paper, which is inspired by the GRU’s ability to capture long- and short-term dependencies in a time series, allowing the GRU to generate signals to compensate errors generated by the GDNN. The GRU-GDNN solver integrates the original GDNN solver with the GRU module and avoids complex computations associated with matrix inversion and time-derivative information when solving TVLEs. Finally, the feasibility and superiority of the GRU-GDNN model are validated through numerical examples and a robot trajectory tracking application.