Numerical simulations of a spinning projectile with a diameter of 120 mm were conducted to predict the aerodynamic coefficients, and the CFD results were compared with the semiempirical method, PRODAS. Six coefficients or coefficient derivatives, including zero and the quadratic drag coefficient, lift force coefficient derivative, Magnus force coefficient derivative, overturning moment coefficient, and spinning damping moment coefficient, which are important parameters for solving the equations of motion of the spinning projectile, were investigated. Additionally, the nonlinear behavior of these coefficients and coefficient derivatives were analyzed through the predicted flow fields. The considered Mach number ranges from 0.14 to 1.2, and the nondimensional spinning rate (PD/2V) is set to 0.186. To calculate the coefficient derivative of the corresponding force or moment, additional simulations were conducted at the angle of attack of 2.5 degrees. The simulation results were able to predict nonlinear behavior, the especially abrupt change of the predicted coefficients and derivatives at the transonic Mach number, 0.95. The simulation results, including the skin friction, pressure, and velocity field, allow the characterization of the nonlinear behavior of the aerodynamic coefficients, thus, enabling better predictions of projectile trajectories.