This paper describes numerical efforts to investigate combustion characteristics of HyShot scramjet combustor, where gaseous hydrogen is transversely injected into a supersonic cross flow. The corresponding altitude, angle of attack, and equivalence ratio are 35-23 km, $0^{circ}$, and 0.426 respectively. Two-dimensional simulation reasonably predicts combustor inner pressure distribution and reveals periodic combustion characteristics of HyShot scramjet combustor. Altitude effects are also investigated and the strength of flow instability and subsonic boundary layer thickness affect the combustion efficiency according to altitudes. Frequency analyses provide the flow instability effects on the turbulent combustion in HyShot scramjet combustor.