The combustion characteristics of a hydrogen-fueled supersonic combustor featuring a large cavity length-to-depth ratio (i.e., 11) were examined by performing experimental trials while varying the fuel injector positions and equivalence ratios. During these trials, flame chemiluminescence images were acquired simultaneously from the side and bottom of the combustor under Mach 2.0 inflow conditions. The flame was observed to stabilize inside the cavity under all conditions. Proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD) analyses of sequential flame chemiluminescence images demonstrated the important effects of oblique shocks induced by fuel injection and heat release on flame stabilization. Because fluctuations in the locations of the flame and of the intense heat release zone were not observed and no dominant frequency was identified in POD and DMD analyses, the present configuration was evidently able to suppress combustion instability. The present research provides preliminary guidance for exploring the feasibility of using cavity combustors with large length-to-depth ratios in scramjet engines.