A solar eruption model coupled with a solar wind is considered. We are interested in how solar eruptions are affected by solar winds during a pre-eruptive phase. To understand it, we performed three-dimensional simulations based on zero-beta magnetohydrodynamic (MHD) equations. As an initial condition, we used a nonlinear force-free field (NLFFF) obtained from a flux emergence simulation result. To initiate a simulation, an upflow is imposed at the top boundary, which develops into a background solar wind in a simulation box. This solar wind eventually produces a solar eruption. From this result, we derive the evolutionary profile of a flux rope and the temporal development of the Lorentz force exerted on a flux rope. We also discuss the application of this model to a real active region by using SDO/HMI data.