Abstract: In order to improve the efficiency and accuracy of slicing STL models for 3D printing, a slicing method to avoid contour intersection is proposed. Firstly, the triangle set on the model intersecting with the tangent plane is extracted, then the intersection points of the triangle set with the tangent plane are calculated and mapped as an undirected weighted graph. Finally, the intersection points of the graph are topologically sorted by depth-first searching algorithm. At the same time, the contour intersection conditions are judged according to the connectivity characteristics of the nodes in the graph, and the intersecting contours are repaired by combining graph and Delaunay triangulation method. Experimental results show that the proposed method can not only deal with the singular cases of contour intersection and accurately obtain the ordered slice contour of each layer, but also can avoid time-consuming reconstruction of mesh topological relations, so the operation efficiency is significantly improved compared with the traditional commercial software.