This study numerically investigated the combustion instability and characteristics of a laboratory-scale gaseous hydrogen-fueled scramjet combustor. For this purpose, a numerical simulation with an improved detached eddy simulation and a detailed hydrogen/oxygen reaction mechanism was performed. The numerical framework used high-resolution schemes with high-order accuracy to ensure high resolution and fidelity. A total of five fuel injection pressures were considered to characterize the combustion instability as a function of the equivalence ratio. A sampling time of up to 100 ms was considered to sufficiently accumulate several cycles of low-frequency combustion instability dynamics with a period in the order of 100 Hz. Numerical results revealed the repetitive formation/dissipation dynamics of the upstream-traveling shock wave, and it acts as a key factor of combustion instability. The period and derived principal frequency of these upstream-traveling shock waves is several ms. The frequency analysis showed that the instability frequency increased in the low-frequency range as the combustion mode transitioned from the cavity shear-layer to the jet-wake type. This characteristic was derived from the transition in combustion mode at the same equivalence ratio. Therefore, it suggests that the instability frequency shifting is governed by the combustion mode rather than the equivalence ratio. These comprehensive numerical results demonstrated not only the effect of the equivalence ratio but also the important role of the combustion mode on the low-frequency combustion instability.