Abstarct: Fuel cells are devices in which chemical energy of fuel directly is converted into electrical energy without combustion. These devices produce less pollution or greenhouse. It is expected that fuel cells have important role in increasing fuel efficiency and reducing dependence on conventional fossil fuels. Fuel cells and electrochemical reactions in them, especially fuel hydrogen, is one of the possible solutions that can improve energy efficiency in the long time and reduce greenhouse gases. Also the significant environmental benefits of them are expected. They are very quiet work that is a very important feature for the use of them in vehicle. In this study proton exchange membrane fuel cell is investigated. This type of fuel cell works at low temperatures that causes start quickly. Also the thikness of it is low therefore it can be compact make. This is consists of three parts namely anode, cathode and electrolyte. The cathode is divided into three subdomains: gas channel (GC), the gas diffusion laxyer (GDL) and the catalyst. Gas diffusion laxyer is a porous medium that composed of a series of carbon fibers whit random positions. In this thesis, pore scale modeling two phase transport in porous gas diffusion laxyer of a proton exchange membrane fuel cell is investigated i.e., modeling structure of porous medium. In this study, Lattice Boltzmann Method (LBM) is used to examine two phase flow in a gas diffusion laxyer. Utilizing of mixed wettability i.e., containing both hydrophilic and hydrophobic pores is the goal of this thesis that the suitable case is introduced. This case is suitable place of hydrophilic fibers, thikness of them and contact angle of hydrophobic fibers. The hydrophilic fibers by considering their place and thikness can improve or reduce the efficiency of fuel cell. The results show that if hydrophilic fibers are placed near gas channel, the efficiency of fuel cell will be better. For example, if these fibers with thikness 50 micrometer are placed in GDL-GC interface (suitable case), the time required for liquid water to reach the GDL-GC interface and liquid water saturation are reduced about 17% and 19% than purely hydrophobic GDL.