Most space manipulators are 7-degree-of-freedom (7-DOF) offset manipulators. It is difficult to find the analytical solution with arm angle parameterization. In this paper, an efficient inverse kinematic strategy with arm angle parameterization is proposed. Firstly, the analytical solution with joint angle parameterization, the definition of arm angle, and the approximate analytical solution with arm angle parameterization are introduced, which paves the way for the following research. Secondly, the proposed inverse kinematic strategy with arm angle parameterization is described in detail. This strategy transforms the inverse kinematics into a nonlinear equation, which is solved by Newton downhill method with variable magnitude. Lastly, the validity and efficiency of this strategy are verified by cases of the 7-DOF offset space manipulator.