In this paper, a polymer electrolyte membrane fuel cell (PEMFC) stack control study is presented. The goal is to track the transient power demand of a real fuel cell (FC) vehicle while ensuring safe and efficient operation. Due to the dynamically changing power demand, fast transients occur in the internal states of the fuel cell (e.g., pressure, humidity, reactant mass) leading to degradation effects (e.g., high/low membrane overpressure, reactants starvation) which are avoided by imposing safety constraints. Efficiency is considered in terms of internal voltage losses minimization as well as minimization of the power of the compressor used to pressurize the cathode. For solving the optimization problem of power demand tracking, adhering to safety constraints, and maximizing efficiency, model predictive control (MPC) has been chosen. Due to the nonlinearity of the FC system, a successive linearization based MPC (SLMPC) is used to control the FC throughout its operating region. Simulation results show that the power demand can be fulfilled while at the same time ensuring safe operation in terms of adhering to constraints and that the minimization of internal voltage losses and compressor power lead to an approximate 9.5% less hydrogen consumption than in the actual reference vehicle.