Investigation of the flow field surrounding supersonic non uniform flying body is a challenge to the aerodynamics researchers. Such investigation by the traditional experimental technique in the wind tunnel is a time consuming and costly. The alternative option is the CFD simulation. This work deals with prediction of the primitive variables of supersonic flow over a missile body, which has a complex profile. Finite difference computational fluid dynamic methods were adopted to solve the governing equations of supersonic, inviscid, compressible, and three-dimensional flow over a missile body with no canard. To deal with complex shape of missile, the "body fitted coordinate system" technique is considered to convert the generated grid from space physical domain to 3-D computational domain. Time-marching MacCormack's explicit technique is used to solve the set of the finite difference discretization equations. The analysis was carried out at 1.5 Mach number. The numerical procedure adopted for this application is found to be capable to capture the shock waves created over the missile body. The explicit technique required about 4000 time steps to achieve the converged solution. The velocity and temperature results showed a good agreement with previously published results. The same approach can be adopted to solve for different Mach numbers for the same missile shape.