Laser-supported detonation (LSD) waves are important because they can generate the high pressures and high temperatures necessary for laser propulsion systems. Although CO₂ laser beams, which have a wavelength of 10.6 μm, have been considered to be one of the most powerful sources of LSD waves, a glass laser beam (1.053μm), for example, also have high power. In this study, we numerically simulated LSD waves propagating through a diatomic gas, in order to evaluate the effects of incident laser wavelength on the construction of the LSD wave. We used the physical-fluid dynamics scheme, which has been developed for simulating unsteady and nonequilibrium LSD waves propagating through hydrogen gas.