This work introduces a novel training strategy for Gaussian Process (GP) models aimed at improving their predictive accuracy and uncertainty quantification capabilities over extended prediction horizons. This improvement is highly relevant for applications in model predictive control (MPC) in the autonomous driving domain. Learning-based MPC strategies typically rely on standard physics-based models augmented with GP models to account for residual nonlinearities and uncertainties not captured by the former. Nonetheless, these conventional approaches often struggle with long-term prediction accuracy, especially when faced with out-of-distribution scenarios, a phenomenon where the model encounters data points that are significantly divergent from the training set. To address these challenges, a multi-step Gaussian process training framework is proposed. This framework yields a GP model capable of making accurate long-term predictions, i.e. a multi-step Gaussian Process (MSGP) model. It achieves this by integrating the simulation of future dynamics into the training process, allowing for the model’s kernel parameters to be tuned toward long-term dynamics. As a result, the MSGP model not only demonstrated the ability to make more stable and accurate long-term dynamic predictions but also with greater confidence. The efficacy of the multistep training framework is shown by the significant improvements in long-horizon dynamics predictions by the MSGP model, achieving an average 19% reduction in mean error and a 90% reduction in variance compared to the standard GP model. Moreover, the efficacy of the MSGP model is further confirmed through its application in a Multi-Step Gaussian Process-based Model Predictive Contouring Controller (MSGP-MPCC), which outperforms a traditional GP-based MPCC (GP-MPCC) baseline controller in lap time and reliability, achieving a 100% success rate in completing laps across ten consecutive simulations without crashing.