Composite polymer electrolyte membranes were prepared with poly (vinyl alcohol) (PVA). Two different molecular weight (Mw), 67·103 and 130·103 g·mol−1 were selected, cross-linked with sulfosuccinic acid (SSA) and doped graphene oxide (GO). The effects on the membranes obtained from these polymers were characterized in order to evaluate the fuel cell performance. Electron microscopy showed a proper nanoparticle distribution in the polymer matrix. The chemical structure was evaluated by Fourier transform infrared spectroscopy. The absence of a crystalline structure and the enhancement on the thermal stability with the addition of 1% of GO was demonstrated by thermal characterization. Total transference number and protonic conductivity were correlated to the performance of a hydrogen fuel cell. Overall, a power increase in the composite membranes with lower molecular weight was observed. Shorter polymer chains may improve protonic conductivity and consequently the fuel cell performance.