In the present study, numerical simulations were performed and compared with experimental results for transonic and supersonic flows past a cone-cylinder and a spherically blunted cone-cylinder. An axisymmetric numerical code was applied to solve the flow around a cone-cylinder, where Roe's flux difference splitting with MUSCL-type approach for higher order was employed. It was confirmed that it produced sufficient accuracy for the present problem. As a result of applying this method to the flow around a spherically blunted cone-cylinder, a weak recompression wave could be successfully captured on the cone. Furthermore, the effect of curvature radius for forebody on the drag coefficient was examined. Consequently, it was found that the drag coefficient is unexpectedly insensitive to the curvature radius at a Mach number of 1.4 although it takes a minimum value at the ratio of curvature to cylinder radius. r/R=0.4. On the other hand it showed rapid increase at r/R<0.4 for Mach number of 1.9.