The mass accommodation coefficient (MAC), a parameter that quantifies the possibility of a phase change to occur at a liquid-vapor interface, can strongly affect the evaporation and condensation rates at a liquid surface. Due to the various challenges in experimental determination of the MAC, molecular dynamics (MD) simulations have been widely used to study the MAC on liquid surfaces with no impurities or contaminations. However, experimental studies show that airborne hydrocarbons from various sources can adsorb on liquid surfaces and alter the liquid surface properties. In this work, therefore, we study the effects of organic surface contamination, which is immiscible with water, on the MAC of water by equilibrium and nonequilibrium MD simulations. The equilibrium MD simulation results show that the MAC decreases almost linearly with increasing surface coverage of the organic contaminants. With the MAC determined from EMD simulations, the nonequilibrium MD simulation results show that the Schrage equation, which has been proven to be accurate in predicting the evaporation/condensation rates on clean liquid surfaces, is also accurate in predicting the condensation rate at contaminated water surfaces. The key assumption about the molecular velocity distribution in the Schrage analysis is still valid for condensing vapor molecules near contaminated water surfaces. We also find that under nonequilibrium conditions the adsorption of the water vapor molecules on the organic surface results in an adsorption vapor flux near the contaminated water surface. When the water surface is almost fully covered by the model organic contaminants, the adsorption flux dominates over the water condensation flux and leads to a false prediction of the MAC from the Schrage equation.