To investigate the aerodynamic characteristics of the free-rotating wraparound fins projectile, the time-precise unsteady numerical simulation of wraparound fins projectile was carried out by using computational fluid dynamics method and slip grid technique. The literature review was compared and synthesized in order to verfiy the validity of the simulation; the appropriate number of grids and time steps were determined using grid-independent and time-step-independent tests, respectively. The difference in aerodynamic characteristics bewteen free-rotating wraparound fins projectile and fixed wraparound fins projectile were compared and analyzed at different Mach numbers; considering different wing and body differential roll conditions, the effects of differential roll angular velocity on the aerodynamic moment characteristics of free-rotating wraparound fins projectile were studied. The results show that the roll moment coefficient and the Magnus moment coefficient of the free-rotating wraparound fins projectile are significantly smaller than those of the fixed wraparound fins projectile due to the different strengths of the viscous vortices at the connection between the wing and the body; at Mach numbers 0.8 and 1.1, the Magnus moment coefficient of the free-rotating wraparound fins projectile is close to 0, and its roll moment coefficient is basically linearly related to the differential roll angular velocity, while the Magnus moment coefficient is significantly non-linearly related to the differential roll angular velocity. The roll moment coefficient of the free-rotating wraparound fins projectile is sharply reduced with the increase of Mach number and the Magnus moment coefficient is sharply increased with the increase of Mach number due to the influence of the viscous vortex at the wing and body joint. The above-mentioned factors have a great influence on the aerodynamic characteristics of the wraparound fins projectile, and should be taken into account in the aerodynamic and ballistic design.