We investigate dynamics of exact N-soliton trains in a spin chain driven by a time-dependent magnetic field by means of an inverse scattering transformation. The one-soliton solution indicates obviously the spin precession around the magnetic field and periodic shape variation induced by the time-varying field as well. In terms of the general soliton solutions, N-soliton interaction and particularly various two-soliton collisions are analyzed. The inelastic collision by which we mean the soliton shape change before and after collision appears is generally due to the time-varying field. We, moreover, show that complete inelastic collisions can be achieved by adjusting spectrum and field parameters. This may lead to a potential technique of shape control of soliton.