Composites used in many fields today are produced by different methods and have different surface curvatures and geometries. Thus, these materials can exhibit different behaviors in terms of machinability characteristics as well as mechanical tests. Drilling operation is an inevitable process for assembly operations of many parts, and in some cases, concave/convex composite parts must also be drilled. In this study, drilling machinability of flat, convex, and concave curved carbon fiber reinforced plastics were investigated experimentally. The machinability was evaluated considering thrust force, delamination formation, and borehole damage analysis. The experimental results demonstrate that the largest thrust force and damage occurs when drilling the flat surface, while the least ones occur when drilling the concave curved surface, in general. In addition, while the damage caused by drilling is severe on the flat surface, higher quality holes were obtained on the concave curved surface at the same cutting parameters.