A variable gain sliding mode control algorithm is proposed for a space robot to track the path aimed at capturing a target. MATLAB/Simscape is used to verify the dynamic model of the space robot and the control algorithm. First, Lagrange method is adopted to establish the dynamic model, and subsequently a model considering the uncertainty of the system is developed. A sliding mode controller which introduces a variable gain is developed. The gain can adapt to the uncertainty of the system and its motion thereby facilitating the controller to be robust. Further, the theoretical model of the space robot is verified using Simscape Multibody. In addition, for the scenarios of single joint motion, multiple joints motion and uncertain system, the proposed control method is applied to the robot for tracking a desired path. Numerical results have demonstrated that in comparison with computed control method, the new method presents higher control accuracy and faster convergence speed.