The article addresses the LPV control of a Polymer Electrolyte Membrane Fuel Cell (PEMFC). In order to optimize efficiency, PEMFCs require reliable control systems ensuring stability and performance, as well as robustness to model uncertainties and external perturbations. On the other hand, PEMFCs present a highly nonlinear behavior that demands nonlinear and/or adaptive control strategies to achieve high performance in the entire operating range. Here, a linear parameter varying (LPV) gain scheduled control is proposed. The control is based on a piecewise affine LPV representation of the PEMFC, a model that can be available in practice. In order to deal with the saturation of the control action, an LPV anti-windup compensation is also proposed. The complete control strategy is applied to several experimental practical situations in a laboratory fuel cell system to evaluate its performance and the reliability of the proposed algorithms.