The droplet motion in a microchannel with different contact angles, which is applicable to a typical proton exchange membrane fuel cell (PEMFC), was studied numerically by solving the equations governing the conservation of mass and momentum. The gas-liquid interface or droplet shape was determined by a level set method which was modified to treat the static and dynamic contact angles. The matching conditions at the interface were accurately imposed by incorporating the ghost fluid approach based on a sharp-interface representation. Based on the numerical results, the droplet dynamics including the sliding and detachment of droplets was found to depend significantly on the contact angle. Also, the effects of inlet flow velocity, droplet size and side wall on the droplet motion were investigated.