Results from numerical simulations of supersonic combustion of H2 are presented. The combustor has a single stage fuel injection parallel to the main flow from the base of a wedge. The simulations have been performed using FLUENT. Realisable k-ε model has been used for modelling turbulence and single step finite rate chemistry has been used for modelling the H2-Air kinetics. All the numerical solutions have been obtained on grids with average value for wall y+ less than 40. Numerically predicted profiles of static pressure, axial velocity, turbulent kinetic energy and static temperature for both non-reacting as well as reacting flows are compared with the experimental data. The RANS calculations are able to predict the mean and fluctuating quantities reasonably well in most regions of the flow field. However, the single step kinetics predicts heat release much more rapid than what was seen in the experiments. Nonetheless, the overall pressure rise in the combustor due to combustion is predicted well. Also, the k-ε model is not able to predict the fluctuating quantities in the base region of the wedge where there is strong anisotropy in the presence of combustion.