One of the weaknesses of the fuel cell is the phenomenon of carbon deposition when using hydrocarbon fuel. Investigating the factors affecting the amount of carbon deposition can improve the performance of the fuel cell, efficiency and life time. A time-dependent two-dimensional numerical model based on the finite element method that considers the carbon deposition has been developed to evaluate the effect of velocity, temperature and hydrogen mole fraction as fuel constituent on the carbon deposition rate and porosity variations. The results were found in good agreement with the available published experimental and numerical data in terms of cell operating voltage, power density and carbon deposition rate. The carbon deposition rate accelerates with increasing operating temperature, inlet molar fraction of hydrogen, and decreasing the inlet velocity. Carbon deposition reduces porosity and catalyst activity. Due to the above mentioned variations, the electric power generated by the fuel cell is drastically reduced, leading to reduced electric efficiency.