A robust Navier-Stokes code has been developed to efficiently predict hypersonic flows in chemical nonequilibrium. The HLLE+ flux discretization scheme is used to improve accuracy and robustness of hypersonic flow analysis. An efficient LU approximate factorization method is also used to solve the flow equations and species continuity equations in fully coupled fashion to implicitly treat stiff source terms of chemical reactions. The HLLE+ scheme shows lower grid dependency for the wall heating rates than other schemes. The developed code has been used to compute chemical nonequilibrium air flow through expanding hypersonic nozzle and past two and three dimensional blunt-nosed bodies. The results are in good agreement with existing numerical and experimental results.