Abstract: The peak of local thermal load might be severe due to the interactions of hypersonic shock wave and turbulent boundary layer. It has significant effect on the aerodynamic performance and flight safety of vehicle. Most previous studies on the interaction in hypersonic condition were based on the Reynolds-averaged methods, the corresponding direct numerical simulation is relatively scarce. The direct numerical analysis of hypersonic shock wave and turbulent boundary layer interaction are helpful to the understanding of the relevant mechanisms and the improvement of existing turbulent modes and sub-grid stress models. Numerical analysis of hypersonic shock wave and turbulent boundary layer interactions in a 34° compression ramp are carried out by means of direct numerical simulation for a free-stream Mach number $M_{\mathbf{\infty }}=6.0$. Based on the Reynolds stress anisotropy tensor, the evolution of turbulent boundary layer along the compression ramp is analyzed. The compressibility effects on turbulent kinetic energy and its transport mechanism are studied through item by item analysis of transport equation. Using dynamic mode decomposition method, the characteristic of unsteadiness in the interaction region is investigated. It is found that along the flow developing downstream, the turbulent state in the near wall region is gradually turned into two-component turbulence from two-component axisymmetric state. The turbulence in outer region approaches the isotropic state from axisymmetric expansion. The results exhibit that there exist significant compressibility effects in the interaction region. The pressure-dilation correlation in turbulent kinetic energy budgets is enhanced significantly. However, it has little effect on the dilatational dissipation. The low-frequency oscillation in hypersonic compression ramp is characterized by the breathing motion of separation bubble. According to the spatial structure of low frequency dynamic modes, the unsteadiness is strongly associated with the separated shear layer.