A test particle study of Landau damping of steepening large-amplitude magnetosonic waves is carried out. Motions of test particles in a model steepning large-amplitude mangetosonic wave are traced. The kinetic energy change of the ensemble of test particles is computed to estimate an effective Landau damping rate of the magnetosonic wave. The numerical results are compared with the linear kinetic theory of Landau damping and interpreted in terms of a simple physical picture for particle trapping.