Aiming at the problem of unbalanced contact force and vibration that affects the grasping stability of multi-arm space robots, a force distribution and compliance control strategy is proposed. Firstly, the force balance conditions for stable grasping is analyzed, the safety factor based on the friction cone constraint is designed, which is then introduced into the force optimization model to distribute the grasping force, so as to minimize the force under the condition of stable grasping. Secondly, the causes of vibration in the grasping transition process are analyzed, then the end effector's output force control strategy based on kinetic energy consumption is designed to achieve rapid vibration suppression and compliant grasp. Furthermore, the control-law switching strategy is designed, so that once the contact-separation phenomenon occurs during the grasping transition process, the end effector can be quickly guided to return to the surface of the goal object. The simulation shows that the proposed method not only improves the stable grasping's safety margin, but also significantly reduces the vibration amplitude, duration and maximum contact force of the end effector, improving the stability and compliance of the multi-arm space robot for target grasping operations.