Compared with traditional non-redundant robots, redundant robots have higher flexibility. In order to make full use of the robot"s redundancy, tasks need to be inserted and removed, so that the robot can complete complex tasks in an unstructured environment. However, the robot velocity would be discontinuous during the task state switching. In response to this problem, this paper is based on the iteratively successive projection mechanism, a iteratively successive projection multi-task priority algorithm is proposed, which can ensure the continuity of joint velocity as tasks switch between inactive and active states, so as to ensues low priority tasks as much as possible within the ability of redundancy. At the same time, based on Lyapunov"s stability theory, the stability of the proposed iteratively successive projection multi-task priority algorithm is proved under the condition that the number of iterations tends to infinity. The trajectory tracking task of the six-bar planar manipulator in the presence of obstacles is simulated, which verifies the continuity and stability of the proposed method.