A two-axis horizontal frame coarse tracking was designed using the application requirements of space debris capture systems. A PI speed loop control method based on closed-loop acceleration was proposed to realize closed-loop high bandwidth control and high-precision tracking accuracy. First, the horizontal coarse tracking frame was designed based on the beam propagation path and geometric load size requirements. The model of the single-axis structure was simplified, and a dynamic equation for the simplified model of the damping stiffness of the two-dimensional single axis was established. Subsequently, vibration analysis was performed to determine the resonance frequency, locked rotation frequency, and main structural parameters of the tracking frame. Third, a double closed-loop control system with velocity and acceleration feedback was designed, and the parameters of the control system were determined. Finally, a performance test of the control system was conducted. The results showed that the control system meets the performance demands. The bandwidth of the control system was 28.2% greater than that of the PI speed loop control system. The PI speed loop control system based on closed-loop acceleration improved the adjustment time by 78.6% and reduced the overshoot by 94.08%. The PI position loop control system based on closed-loop acceleration had an adjustment time of 0.085 s and an overshot of 11.66%, which exhibited a small tracking error and strong antiinterference ability.