Hybrid electric vehicles (HEVs) gain more and more attention, as they represent a more environmental friendly alternative to conventional vehicles. If combined with photovoltaic panels, they can lead to further reduction of emissions. The paper focuses on a solution for minimizing the fuel consumption in a series hybrid solar vehicle (HSV). After briefly introducing the model, first a global optimum in fuel consumption is presented using dynamic programming, as a reference value. As a real-time control strategy, model predictive control (MPC) is considered. A fuel consumption equivalent quantity is defined which is used for calculating the fuel needed to bring the battery state of charge to a starting value (set in this case for 0.7 in relative units). For different values of the MPC tuning parameters simulations are performed using the urban section of the New European Drive Cycle. Conclusions based on the simulations are presented.