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An improved K-ω model, which allows for compressible corrections, is proposed in this paper. Numerical scheme was established utilizing the improved Total Variation Diminishing (TVD) scheme and applying implicit scheme to the negative source terms of the turbulence model. Hypersonic flat-plate boundary-layer flows and hypersonic compression ramp flows marked with separation, reattachment and shock/boundary layer interactions are then computed. Comparisons between the computational results, the experimental results and the semi-empirical formulations show that the compressible correction term of the K-ω turbulence model is a pressure-dilatation correlation. In addition, for flow with separation and without separation, calculation results of wall pressures, friction coefficients and wall heat transfer rate distributions using the improved model and established scheme agree better with the experimental results than that using the original K-ω model.