An improved ghost-cell immersed boundary method proposed in this paper, coupled with a high order finite difference solver, is applied to simulate the supersonic compressive flows around the complex obstacles.The main improvement of this algorithm is the treatment of the solid boundary that both ghost points inside the solid domain and forcing points inside the fluid domain due to the extension of the boundary are chosen to reconstruct the flow information considering the effect of solid wall on fluid.This brings refined boundary with discrete points and strengthens the wall conditions, which plays the role of local mesh refinement.The fluid points are limited in a certain source space as the interpolating points of the inverse distance algorithm, which effectively avoids the fact that the interpolating points are too few to possibly lead to coincide with the forcing points.Two problems of two dimensional shock reflection (Ma=
2.81) and three dimensional flow around the smooth sphere (Ma=
1.2) demonstrate the significant improvement of the numerical accuracy compared to the general ghost cell method. The results reveal the instability mechanism of the free shear layer as a result of the interaction between the shear layer, the compression wave system and the wake. The thickness and Reynolds fluctuation of the shear layer experience three regimes of linear growth, large amplitude oscillation and small amplitude fluctuation, resulting in an exponential growth of wrinkling factor.The turbulent structure near the shear layer shows obvious anisotropy because the streamwise Reynolds normal stress is dominant and a spatial hysteresis exists in the effect of the tail shock on Reynolds normal stresses in different directions.