Combustion characteristics in a supersonic combustor with normal and angled hydrogen injection upstream of a cavity flameholder are investigated numerically using a hybrid Reynolds-averaged Navier–Stokes/large eddy simulation method acting as a wall-modeled large eddy simulation. A turbulent incoming boundary layer with thickness of δinf = 2.5 mm is considered and a recycling/rescaling method is adopted to treat the unsteady inflow. Three injection angles, α = 30°, 60° and 90°, are considered. The results show that combustion efficiency increases with increasing injection angle since the fuel jet with larger injection angle tends to benefit more from the close coupling of flow, mixing and combustion. Moreover, it is found that the heat release distribution in the streamwise direction is more uniformly for larger injection angle than for lower injection angle, which tends to result in higher total pressure recovery in the far downstream regions for larger injection angle as uniformly-distributed heat release seems beneficial to reduce the total pressure loss for the present diffusion combustion.