The tethered space robot (TSR) is a new concept of space robot which consists of a robot platform, space tether and operation robot. This paper presents a multi-objective optimal trajectory planning and a coordinated tracking control scheme for TSR based on velocity impulse in the approaching phase. Both total velocity impulse and flight time are included in this optimization. The non-dominated sorting genetic algorithm is employed to obtain the optimal trajectory Pareto solution using the TSR dynamic model and optimal trajectory planning model. The coordinated tracking control scheme utilizes optimal velocity impulse. Furthermore, the PID controller is designed in order to compensate for the distance measurement errors. The PID control force is optimized and distributed to thrusters and the space tether using a simulated annealing algorithm. The attitude interferential torque of the space tether is compensated a using time-delay algorithm through reaction wheels. The simulation results show that the multi-objective optimal trajectory planning method can reveal the relationships among flight time, fuel consumption, planar view angle and velocity impulse number. This method can provide a series of optimal trajectory according to a number of special tasks. The coordinated control scheme can significantly save thruster fuel for tracking the optimal trajectory, restrain the attitude interferential torque produced by space tether and maintain the relative attitude stability of the operation robot.