According to the spatial 7 degree of freedom (7-DOF) redundant manipulator with elbow offset, a joint angle parameterized method is proposed to solve the problem. According to the structural characteristics of the space manipulator, the arm type was analyzed, and the Denavit-Hartenberg (D-H) method was used to establish the coordinate system of the space manipulator arm. The D-H method was used to describe the operation space of the space manipulator. Based on the consideration of the kinematic constraint, the forward kinematics model with the joint angle as the variable was obtained. By analyzing the solutions of the inverse kinematics model, the whole analytical method of the inverse kinematics of the manipulator was solved by the analytical method of matrix inverse. In the Matlab environment, the initial attitude of the manipulator was simulated by using Matlab Robotic Tools. Based on the position and pose of the end of manipulator, the angle of each joint of the robot arm was solved by the inverse kinematics algorithm. The inverse kinematics of the manipulator is taken as the basis for the motion planning and trajectory control of the manipulator.