Exact soliton solutions of a modified Landau-Lifshitz equation for the magnetization of conducting ferromagnet in the presence of a spin-polarized current are obtained by means of inverse scattering transformation. From the analytical solution the effects of spin current on the frequency, wave number, and dispersion law of spin wave are investigated. The one-soliton solution indicates obviously current-driven precession and periodic shape variation as well. The inelastic collision of solitons, by which we mean the shape change before and after collision, appears due to the spin current. We, moreover, show that complete inelastic collisions can be achieved by adjusting spectrum and current parameters. This may lead to an potential technique for shape control of spin wave.