This paper is devoted to study the electrochemical behavior of Pt catalyst in a polymer electrolyte fuel cell at various operating conditions and at different electric potential difference (also known as voltage) cycling applied in accelerated stress tests. The degradation of platinum is considered with respect to the Pt ion dissolution and the Pt oxide coverage of catalyst described by a one-dimensional model. In the model, degradation rate increases with temperature and decreasing particle diameter of Pt nano-particles. The theoretical study of the underlying diffusion system with the nonlinear reactions is presented by analytical methods and gives explicit solutions through a first integral of the ODE system. Numerical tests are obtained using a second order implicit-explicit scheme. The computer simulation shows that the lifetime of the catalyst depends on the voltage profile and the upper potential level. By this Pt mass loss is more significant at the membrane surface than at the gas diffusion layer.