With the increasing demand of human beings for space exploration, space robots show great development potential. When grasping space objects with different sizes and shapes, cable-driven continuum arms have better performance than traditional robots. In this paper, a novel space robot with triple cable-driven continuum arms is proposed, which can achieve compliant grasping through multi-arm cooperation. The kinematic model of the robot is proposed and verified through simulations and experiments. Results show that the maximum repeat positioning error is no larger than 1 mm and the maximum tracking error is no larger than 2 mm, compared to the 300 mm long arm. In addition, the demonstration experiment of grasping a ball indicates the good performance of the robot in compliant grasping.