It is of significant importance to calculate the stability derivative accurately for stability and control of an aircraft. Dynamic mesh technology in computational fluid dynamics(CFD) are used to simulate periodic pitching oscillation motion of finned missile circling around a fixed axis. The hysteresis curve of pitching moment coefficient for the basic model Finner missile was obtained at different Mach number. The static derivatives of the missile in different Mach numbers were computed with difference method, line method and Least-square technique. The minimum error can be 0.5% compared with experimental data.; Dynamic stability derivatives were coumputed at different Mach numbers with integral method, Least-square technique and hysteresis-circle method. The error is between 5.8% and 23.8%. The results show that the method in the paper can correctly compute the static and dynamic stability derivative of finned missile and it can make a reference for engineers.