To solve the problem that the manipulator of single-arm space robot has limited accuracy of positioning and attitude determination during on orbit servicing, a precision synergy control algorithm for multi-arm space robot was proposed. This method researched space robot (SR) with three arms each of them has seven degrees of freedom. The kinetic equations include the body and arms were built based on Kane method. Moreover, according to Lyapunov function, a trajectory tracking algorithm was designed for each arm to reduce motion jitter while capturing target. Simulation results show that the presented method can ensure the manipulators move along the desired paths and improve the position and attitude precision of manipulators.