The supersonic flow over a cone is of great. practical importance in applied aerodynamics; Nose cones of many high-speed missiles and projectiles are approximately conical, as are the nose regions of fuselages of most supersonic airplanes. In the present work. a numerical technique for solving the Taylor-and-Maccoll conical flow equation is introduced. Results of the present technique are verified against results of other key researchers. An excellent agreement was found in all cases. The inputs of the present code are the free stream Mach number and the cone half angle. The output includes the velocity field, the pressure field, the shock wave angle, and the stream lines directions. The running time on a Pentium 75Mhz is around 2 CPU-seconds for each case.