Abstract: This paper presents a fast and accurate collision detection algorithm for convex polyhedrons, which employs the method of projection-separating edges based on linear projection. This algorithm improves the algorithm of projection-separating planes. First, this paper proposes the concept of projection-separating lines, and proves the existence of the separating lines in any separated condition. Second, the quasi projection-separating lines set is created from the opposite surfaces on convex polyhedrons, then the problem of the collision detection between 3D convex polyhedron is converted to the collision detection between 2D convex polygons by the projection of the lines; Third, the projection method has been applied to convex polygons and 2D problem is converted to 1D problem. The experimental results show that the proposed algorithm has high detection accuracy and response speed.