Hovering is an effective and challenging way for asteroid exploration. In this paper, the adaptive quasi-periodic switching control method for body-fixed hovering of asteroids with low fuel consumption and strong robustness using constant thrust is proposed. By analyzing the active control process and the drift process of the spacecraft in the phase plane, constant thrust control is applied in the appropriate orientation to maintain the desired hovering state above the asteroids. Considering the uncertainty of the dynamic environments near the asteroids, the apex position of drift process in the phase plane is predicted, meanwhile, the compensation conditions and the calculation formula for the constant-thrust engine ignition are given. The simulation results show that the quasi-periodic switching control method can reduce the fuel consumption of the spacecraft compared with other methods, moreover, the adaptive quasi-periodic switching controller can effectively improve the robustness of the system.