This thesis is concerned with model predictive control (MPC) within the field of autonomous driving. MPC requires a model of the system to be controlled. Since a vehicle is expected to handle a wide range of driving conditions, it is crucial that the model of the vehicle dynamics is able to account for this. Differences in road grip caused by snowy, icy or muddy roads change the driving dynamics and relying on a single model, based on ideal conditions, could possibly lead to dangerous behaviour. This work investigates the use of Gaussian processes for learning a model that can account for varying road friction coefficients. This model is incorporated as an extension to a nominal vehicle model. A double lane change scenario is considered and the aim is to learn a GP model of the disturbance based on previous driving experiences with a road friction coefficient of 0.4 and 0.6 performed with a regular MPC controller. The data is then used to train a GP model. The GPMPC controller is then compared with the regular MPC controller in the case of trajectory tracking. The results show that the obtained GP models in most cases correctly predict the model error in one prediction step. For multi-step predictions, the results vary more with some cases showing an improved prediction with a GP model compared to the nominal model. In all cases, the GPMPC controller gives a better trajectory tracking than the MPC controller while using less control input.