This paper deals with the inverse kinematic solutions of a 7-DOF redundant robot. A hybrid algorithm that can improve the control precision is proposed. This algorithm uses screw theory to describe the motion of the robot. Firstly it finds the joint rate solution through optimizing kinematic performance criterion. Then a special joint is fixed to transform the problem into kinematic control of a non-redundant robot, by using Paden-Kahan subproblems, other joint angles are solved. The effectiveness of the proposed algorithm has been verified by a simulation of a 7-DOF robot.