We conducted high-resolution non-hydrostatic numerical simulations to study the effect of surfactants on near-surface turbulence. Laboratory experiments at the UM RSMAS ASIST facility presented in a companion paper report a reduction of turbulence below the air-sea interface and an increase of the surface drift velocity in the presence of surfactants. We implement the effect of surfactants as a rheological, viscoelastic boundary condition at the surface. Our numerical experiments are consistent with the results of the laboratory experiments. We also simulated the effect of surfactants on the temperature difference across the thermal molecular sublayer (cool skin) and on gas transfer velocity. The numerical simulations demonstrate an increase in the temperature difference across the cool skin and reduction of the gas transfer velocity in the presence of surfactant. The results also reveal the effect of surfactants on the different types of molecular sublayers (viscous, thermal and diffusion), which is important for the development of proper parameterization of the interfacial component of air-sea gas exchange under low and moderate wind speed conditions.