Abstract: Thin superconducting films can exhibit negative magnetoresistance when an in-plane external magnetic field is aligned parallel with the transport current. We explain this effect as due to appearance of parallel vortices in the plain of the film at the first critical magnetic field H-c1 which leads to an enhancement of the superconducting properties and impedes the motion of the current induced perpendicular vortices. Our theoretical results are based on a numerical solution of the time-dependent and stationary 3D Ginzburg-Landau equations.