Computational fluid dynamics (CFD) simulations of a single staged injection of H2 through a central wedge shaped strut and a multi-staged injection through wall injectors are carried out by using Ansys CFX-12 code. Unstructured tetrahedral grids for narrow channel and quarter geometries of the combustor are generated by using ICEM CFD. Steady three-dimensional (3D) Reynolds-averaged Navier-stokes (RANS) simulations are carried out in the case of no H2 injection and compared with the simulations of single staged pilot and/or main H2 injections and multistage injection. Shear stress transport (SST) based on k-ω turbulent model is adopted. Flow field visualization (complex shock waves interactions) and static pressure distribution along the wall of the combustor are predicted and compared with the experimental schlieren images and measured wall static pressures for validation. A good agreement is found between the CFD predicted results and the measured data. The narrow and quarter geometries of the combustor give similar results with very small differences. Multi-staged injections of H2 enhance the turbulent H2/air mixing by forming vortices and additional shock waves (bow shocks).