This paper presents the computations of the pitch dynamic stability derivatives for a projectile with spinning tail fins. The Basic Finner model is chosen to compare the rotating effect of tail fins. Three-dimensional unsteady Reynolds-averaged Navier-Stokes computational fluid dynamics calculations were performed to simulate forced harmonic pitch motion of projectile and rotating motion of its tail fins simultaneously. Numerical results were compared with computational results for tail-fixed cases. The results indicate that the rotation of tail fins decrease pitch damping force coefficients and increase pitch damping moment coefficients significantly. The results also show that the pitch dynamic stability derivatives are strongly affected by rotating speed of tail fins in the subsonic and transonic regimes.