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A compressibility correction for the shear stress transport (SST) model suitable for hypersonic compressible turbulent flows is proposed in this paper. Numerical computations are performed by using an improved TVD scheme, and the negative part of the source terms in the turbulence model is discretized by using an implicit scheme. To validate the corrected model, hypersonic flows over a flatplate, as well as compression ramps with or without separated flows are computed by using the developed model. The numerical results reveal that, in comparison with experimental results and results computed by the original model and semi-empirical formulae, the compressibility effects on the SST model stem from the scalar product of the weighted density average of the turbulent fluctuating velocity and the pressure gradient of the average flow field. In addition, it is demonstrated that the presently established model provides more favorable results on the wall pressure, skin friction and wall heating rate distribution for the experiments than the original SST model and other compressibility modifications. [ABSTRACT FROM AUTHOR]