Abstract: Global linear stability of compressible,three-dimensional flow around a sphere is investigated with a quasi-linearization method on Navier-Stokes equations.An implicit restarted Arnoldi approach is adopted to solve the eigenvalue problem.The global stability problem of three-dimensional compressible basic flows around a sphere is investigated at subcritical parameters of Reynolds number Re=200,Mach number M=0.2,and supercritical parameters of Re=300,M=0.6.It shows that the increasing of Mach number(up to 0.6) has no qualitative influence on transition of flow patterns.