One-dimensional detonation waves supported by a piston are numerically investigated. The analysis is carried out based on the numerical simulation using a finite difference method. A simplified two-step chemical reaction model consisting of the induction and exothermic reactions is used. Two types of unsteady oscillations are observed at the shock front in the simulation results: one shows a high frequency and low amplitude oscillation and the other shows a low frequency and low amplitude one. In the simulation results, the oscillation type does not depends on the intensity of the concentration of the heat release due to the combustion, even though the oscillation type depends on the piston speed. The flow features of the oscillatory shock front are clarified with the x-t diagram. The mechanism obtained in the present study is discussed in comparison with the unsteady phenomena observed as the shock-induced combustion around a hypersonic spherical projectile.