Laser texturing is a relatively new multiprocess technique that has been used for machining 3D curved surfaces; it is more flexible and efficient to create decorative texture on 3D curved surfaces of injection molds so as to improve the surface quality and achieve cosmetic surface of molded plastic parts. In this paper, a novel method of laser texturing 3D curved surface based on 3-axis galvanometer scanning unit has been presented to prevent the texturing of injection mold surface from much distortion which is often caused by traditional texturing processes. The novel method has been based on the computer texture mapping technology which has been developed and presented. The developed texture mapping algorithm includes surface triangulation, notations, distortion measurement, control, and numerical method. An interface of computer texture mapping has been built to implement the algorithm of texture mapping approach to controlled distortion rate of 3D texture math model from 2D original texture applied to curvature surface. Through a case study of laser texturing of a high curvature surface of injection mold of a mice top case, it shows that the novel method of laser texturing meets the quality standard of laser texturing of injection mold.