A real-time robot arm control method for obstacle avoidance is proposed. If links are close to and approaching obstacles, the end-effector velocity is modified so that collision is avoided and the error between the desired and modified end-effector velocity can be minimized. For this purpose, a new matrix called the "collision Jacobian", which relates the approaching velocity of the links to the obstacles with the end-effector velocity, is proposed. Because the modified velocity can be calculated without an iterative algorithm, the proposed method is effective for real-time obstacle avoidance. This method is applied to collision avoidance between the links of a parallel arm.