Abstract: This paper introduces an algorithm for contour-parallel offset tool path linking without tool retractions.The concept of a tool path loop tree is proposed to provide the information on the relationship between parents and children among the tool path loops.We also define a tool path loop in the tree as a vector according to the tool path loop tree,called tool path loop vector.The components of the vector are of attributes of the tool path loop in the tree.Based on the tool path loop vectors and by traveling throughout the tool path loop tree,we could derive an optimal algorithm to obtain a contour-parallel offset tool path without tool retractions.In comparison with other algorithms,our algorithm can obtain a contour-parallel offset tool path without tool retractions and over milling.Besides,the algorithm could run automatically.