To achieve a detailed understanding of the characteristics of the liquid hydrogen-oxygen (LH2/LOX) rocket exhaust plume with afterburning, the three-dimensional compressible Reynolds-averaged Navier-Strokes (RANS) equation with the realizable k-Ɛ turbulence model is applied to calculate the flow field of the supersonic exhaust gas. An optimized 9-species and 14-steps chemical mechanism is used for the afterburning effects. Multi-grid method is adopted to establish structural grid of 8.87 million cells for the finite volume computation. The afterburning model is established under six inflow conditions and then validated by experimental data. The validated model is applied to compare the under-expanded supersonic plume with and without afterburning reaction at different flight altitudes. The simulation results indicate that afterburning mainly occurs in the mixed layer. Compared to the frozen flow, the peak temperature of the reaction flow has increased from 123 K to 318 K, the mole concentrations of hydrogen and water vapor change in the reacting plume. The afterburning has significant influence on the thermal environment of the exhaust plume at low altitude, but its effect becomes weak with the altitude increase. The results have provided a relevant evaluation of the flow field characteristics of supersonic plume and offer some usefulness to further numerical simulations of the liquid rocket exhaust jet with afterburning.