Closed-loop inverse kinematics (CLIK) algorithm mostly resolves the redundancy at the velocity level. In this paper we extend the CLIK algorithm to the acceleration level to meet some applications that require the joint accelerations. The redundancy resolutions at the velocities and acceleration levels via pseudoinverse method are analyzed respectively. The objective function of joint limits avoidance(JLA) is combined into the redundancy resolution as an optimization approach of the null space motion. A seven-DOF redundant manipulator is designed to do the computer simulations and the real experiments are carried out on a Powercube modular manipulator. Their results demonstrated the effectiveness of the proposed algorithm.