Self-collisions of a dual-arm robot system can cause severe damage to the robot. To deal with this problem, this paper presents a real-time algorithm for preventing self-collisions in dual-arm systems. Our first contribution in this work is a novel collision model built using discrete spherical bounding volumes with different radii. In addition, we propose a sensitivity index to measure the distance between spheres with different radii in real time. Next, according to the minimal sensitivity index between different spheres, the repulsive velocity is produced at the centers of the spheres (control points), which the robot uses to generate new motion based on the robot kinematic model. The proposed algorithm offers the additional benefits of a decrease in the number of bounding spheres, and a simple collision model that can effectively decrease the computational cost of the process. To demonstrate the validity of the algorithm, we performed simulations and experiments by an upper-body humanoid robot. Although the repulsive velocity acted on the control points, the results indicate that the algorithm can effectively achieve self-collision avoidance by using a simple collision model.