To meet the micro-newton adjustable thrust requirements of gravitational wave detection tasks, the design concept of micro-newton hall thrusters is analyzed based on the working principle of this electric propulsion technology. After a series of research of thruster size optimization, a micro-newton Hall electric thruster with outlet diameter being 4 mm and the length of 30 mm is designed. The experimental results of the thruster show that the thruster can achieve the continuous adjustable thrust output 0.2~112.7 μN, which meets the requirements of the gravitational wave detection missions. To further improve the dynamic performance of the thruster, the design and simulation of thruster control system are carried out, and the drag-free satellite simulation system is established based on the principle of drag-free control. Simulation results show that the closed-loop control of the thruster can not only effectively reduce the thrust noise and improve the response speed and accuracy of thrust output, but also improve the compensation accuracy of non-conservative forces, so that the displacement errors between spacecraft and test mass could satisfy the drag-free control accuracy indexes of gravitational wave detection tasks. Therefore, this kind of Hall thruster can meet the propulsion requirements of gravitational wave detection tasks and has the possibility to be applied to such space science missions.