Numerical solutions of full Navier-Stokes equations with chemical reaction flow were obtained for a combustion chamber and nozzle flow of the N 2O/HTPB hybrid rocket motor. Lower-Upper decomposition scheme and MUSCL-type and VanLeer approach were used. Two steps chemistry model were adopted. A chemical reaction model with 10 species and 11 elementary reactions was presented The combustion chamber and the nozzle flow at different time were calculated. The combustion character was analyzed by the result, which will be useful for the hybrid rocket motor design. Copyright IAF/IAA. All rights reserved.