A computational fluid dynamics method has been applied to simulate the unsteady aerodynamics of the projectile launched from a ballistic range. A moving coordinate scheme for a multi-domain technique was employed to investigate the unsteady flow with moving boundary. The coordinate system fixed to each moving domain was applied to the multi-domains, and the effect of virtual mass was added in the governing equations for each domain. The unsteady, axisymmetric Euler equation systems were numerically solved using the third order Chakravarthy-Osher total variation diminishing scheme, with MUSCL approach. The projectile mass and configuration effects on the unsteady aerodynamics were investigated based on the computational results. The present computations were validated with results of some other CFD works available. The computed results reasonably capture the major flow features, such as shock waves, blast waves, shear layers, vertical flows, etc. which are generated in launching a projectile up to a supersonic speed. The present computational method properly predicts the velocity, acceleration and drag histories of the projectile.