Numerical study is carried out to investigate the effects of chemistry and thermal radiation on the rocket plume flow field at various altitudes. Navier-Stokes equations for compressible flows were solved by a fully-implicit TVD code based on the finite volume method. An infinitely fast chemistry module for hydrocarbon mixture with detailed thermo-chemical properties and a thermal radiation module for optically thick media were incorporated with the fluid dynamics code. The plume flow fields of a kerosene-fueled rocket flying at Mach number zero at sea-level, 1.16 at altitude of 5.06 km and 2.90 at 17.34 km were numerically analyzed. Results showed the plume structures at different altitude conditions with the effects of chemistry and radiation. It is understood that the excess temperature by the chemical reactions in the exhaust gas may not be ignored in the view point of propulsion performance and thermal protection of the rocket base, especially at higher altitude conditions.