Combustion phenomena in a ramjet combustor with cavity flame-holder is studied numerically. Combustor follows a constant area isolator and comprises of hydrogen fuel injected sonically upstream of the cavity. Secondary fuel injection is performed at the cavity backwall A diverging section follows the cavity to prevent thermal choking. These concepts are also utilized in practice. Calculations were performed for an entrance Mach number of 1.4. Stagnation temperature is 702 K, corresponding to a flight Mach number of 3.3 at an altitude of 12.5 km. Detailed chemical kinetics are taken into account with a reaction mechanism comprising of 9 species and 25 reaction steps. Turbulence is modeled using Menter's k - omega shear stress transport model, which is appropriate for high speed internal flows. It is observed that flame anchors at the leading edge of the cavity, and the flame is stabilized in the cavity mode rather than the jet-wake mode. Numerical simulation captures all the essential features of the reacting flowfleld.