A neural network is presented here to detect the existence and measure the degree of intersection between two convex polyhedra. It can be implemented in hardware with very simple analog/digital circuits. The convergence and stability of the neural network is studied by the Lyapunov (energy function) approach. A combined simulation test and hardware speed comparison indicates that the netural network has a very attractive high speed/cost ratio. When applied to collision detection, it keeps approximately the same speed as the two most efficient algorithms in the literature. The neural network can also provide additional information on the degree of collision and the best direction to separate two colliding polyhedra, though it causes more average iteration steps. Yet its simple integer or analog operations require a shorter computation time. When integrated in a highly parallel system, the neural network drastically reduces the average collision detecting time with little increase in implementation cost.