Polyhedral surfaces are used as representation model for CAM and process planning purposes because of its simplicity for data exchange and geometric computation. However, there is few tool path planning strategies for such surfaces but the iso-plane method. In this paper, contour parallel path are generated for three-axis ball-end milling. This tool path is based on a novel algorithm for offsetting curves on polyhedral surfaces presented in this paper. It reduces the task of removing complex interfering of offset curve from 3D surface to 2D plane by flattening mesh surface, and avoids costly 3D Boolean set operations and expensive distance calculation. This results in an efficient tool-path generation. Empirical examples illustrate the feasibility the proposed method.