This paper numerically investigated the dynamic characteristics of combustion in a model scramjet. Three-dimensional compressible large eddy simulation was performed on a hydrogen fueled combustor and pressure fluctuations were recorded. The analysis of pressure data showed that the combustion processes are intrinsically unstable under supersonic air inflow conditions. Flame dynamics were convinced by the fluctuations in flame lift-off distance away from the strut base. Combined with the corresponding time interval, instantaneous flame speed was calculated. Results indicated that pressure oscillations at different locations show difference in amplitude, frequency, and the underlying control mechanism. Flame front oscillation analysis showed that the flame–shock interaction in the strut recirculation zone was responsible for the combustion instability. Flame dynamics were compared with low-speed turbulent lifted flames. The transition between flame propagation just after the strut and shock-induced combustion in the subsonic bubble at the intersection of two wall-reflected oblique shocks made for the flame stabilization. •The reasons for pressure oscillation at different locations are distinguished.•Flame lift-off distance and the instantaneous flame speed are quantified.•Intermittent formation of subsonic bubble controls the combustion oscillation.•Flame propagation and shock-induced combustion jointly stabilize the flame.