The vehicle dynamics model serves as a vital component of autonomous driving systems, as it describes the temporal changes in vehicle state. In a long period, researchers have made significant endeavors to accurately model vehicle dynamics. Traditional physics-based methods employ mathematical formulae to model vehicle dynamics, but they are unable to adequately describe complex vehicle systems due to the simplifications they entail. Recent advancements in deep learning-based methods have addressed this limitation by directly regressing vehicle dynamics. However, the performance and generalization capabilities still require further enhancement. In this letter, we address these problems by proposing a vehicle dynamics correction system that leverages deep neural networks to correct the state residuals of a physical model instead of directly estimating the states. This system greatly reduces the difficulty of network learning and thus improves the estimation accuracy of vehicle dynamics. Furthermore, we have developed a novel Transformer-based dynamics residual correction network, DyTR. This network implicitly represents state residuals as high-dimensional queries, and iteratively updates the estimated residuals by interacting with dynamics state features. The experiments in simulations demonstrate the proposed system works much better than physics model, and our proposed DyTR model achieves the best performances on dynamics state residual correction task, reducing the state prediction errors of a simple 3 DoF vehicle model by an average of 92.3% and 59.9% in two dataset, respectively.