Collision detection algorithms play a very important role in the field of robot path planning. In a simulation system of intelligent robot, collision detection takes up a large portion of the time for the robot to plan a complete path from the initial position to the final position. So how to reduce the time the robot uses to detect collision becomes a key problem. But collision detection finally will transform to a problem to determine whether the intersection of two convex regions formed by linear inequalities is empty or not. The authors present a new algorithm in this paper. Firstly, a vector pointing from one polyhedron to the other is picked. Then the authors start to find an intersection plane of one polyhedron based on the scalar product of the norm vector of the plane and the picked vector. If such a plane is found, the intersection of the two convex polyhedra is not empty.