The unsteady Navier-Stokes equation and rigid body dynamic equations are solved to simulate the flight trajectory of a spinning projectile. The unsteady aerodynamic computations uses an in-house hybrid unstructured Navier-Stokes flow solver (HUNS3D). The rigid body of 6-DOF motion equations are solved using an advanced Adams prediction-correction method. The Coupled Computation Method is applied to simulate and analyze the flight trajectory of U.S. Army Research Laboratory spinning projectile test model. Computed results are found to be generally in good agreement when compared with experiment data and reference numerical results.