This paper presents a fast continuous collision detection algorithm to dealing with moving multiple convex objects within a period of time, which is based on the Gilbert-Johnson-Keerthi algorithm. The algorithm is determined by whether the minimum distance between the two objects within a period of time is zero to detect the occurrence of a collision. First, the algorithm utilizes GJK algorithm to calculate the minimum distance between the two objects and to detect the collision in finite steps. If two objects collide, then, determine the precise collision position of two objects based on the ray-casting algorithm, and respond according to the environmental requirements, adjust two objects' location. The simulation results show that this algorithm has high real-time and accurate characteristics for continuous collision detection between multiple moving objects.