The fuel cell is an electrochemical device that converts the chemical energy of hydrogen into electric energy. When the fuel cell is in stationary operation hydrogen and oxygen or air must be constantly supplied to cell in order to keep the chemical reaction going on continuously, then cell gives DC voltage. The fuel cell is powered by hydrogen and oxygen gas, while it produces electricity and as a byproduct of the reaction we get water and waste heat, because the reaction is exothermic . The great advantage of a fuel cell is that it directly converts chemical energy into electrical in only one step, which is one of reason why it has high efficiency. The fuel cell is a very simple construction and there is no moving element. The central part of the PEM (Proton Exchange Membrane) fuel cell is an electrolyte, a proton conducting membrane. Membrane is located between the anode and cathode electrodes, behind the electrodes are electrically conductive porous layers which are used for transport of gases and electrons. All of this is confined in a graphite mold that carries electrons and heat. Hydrogen in form of gas goes to anode through the anodic porous layer and then is dissociated into 2 proton and 2 electrons. Electrons travel trought the graphite layer and goes to catode electrode while it perform useful work, we get the difference in electrical potential at the output of the cell. On the other side, the protons that are formed on the anodes pass through the membrane to the cathode where they are connected with the oxygen coming from the cathode porous layer and the electrons that came in the outer circuit and thus formed a water molecule. Non-equilibrium thermodynamics is the branch of a thermodynamics that describes systems that are not in global equilibrium. It describes transport processes and energy conversions in time, unlike equilibrium thermodynamics that describes only the equilibrium states frozen in time. In non-equilibrium thermodynamics we assume the existence of a local equilibrium, which means that thermodynamic quantities change continuously and we have well defined laws of thermodynamic on that scale. The basic quantitie of the non-equilibrium thermodynamics is the entropy production, with the help of the conservation laws expressed in the local form we can use it to describe all the processes in the system. In this paper linear non-equilibrium thermodynamics has been applied to theoretically describe the fuel cell in stationary work to get profiles of temperature, electrical potential and chemical potential, and the molar fraction for several instances of output current density . We start with derivation of conservation laws expressed in the local form, then expresing the entropy production in form of conjugated flows and forces. In the next step a one-dimensional mathematical model of PEM fuel cell has been set up, and finally the total entropy production is calculated by summing up the individual contributions in fuel cell. Finally, the total entropy production was calculated by summing up the individual contributions and the graphs of changes of all values.