A Learning-based Model Predictive Control (LMPC) algorithm is proposed for a Formula Student (FS) autonomous vehicle. The online learning algorithm has two distinct roles: to improve the dynamic model accuracy of the vehicle used in the MPC, while performing online tuning of the model predictive controller parameters. The developed controller is shown to reduce the total lap time through an iterative learning process as the vehicle progresses on track. To capture the full complexity of the nonlinear higher order dynamics, an Artificial Neural Network (ANN) complements the vehicle’s nominal model. The ANN is trained using an online supervised learning scheme based on past model prediction errors. Additionally, a Genetic Algorithm (GA) is used to iteratively find the optimal set of controller parameters that maximizes a reward function. Several simulation tests performed on real examples of competition tracks demonstrate the effectiveness of the approach. Moreover, it is shown that the combination of both online learning methods is able to significantly improve tracking performance of the FS vehicle, eventually reducing the total lap time by over 16%.