Numerical simulation for the detonation wave propagation in a two-parallel-plane combustor is conducted to investigate the effect of curvature. Governing equations are two dimensional euler equations with reduced kinetic reaction model. The length of the injection wall is fixed at 40 mm and curvature is changed as a parameter. Moreover, injection gas is stoichiometric premixed gas and non-premixed gas. The following knowledge is obtained through the calculation. The pressure at the detonation front becomes gradually smaller in larger curvature. It affects the height of the injected propellants to be smaller. Propagation velocity decrease occurs at the larger curvature, and this tendency does not depend on the injection method. The degree of this effect is larger in the non-premixed injection cases. Furthermore, the whole region analysis is conducted to confirm the effect of periodic boundary. The results are different from the cases of using periodic boundary, and similar phenomenon is observed in the experiments.