Based on topographic images of the GaAs(110) surface obtained by non-contact atomic force microscopy (NC-AFM) with different tip–sample distances, we discuss the tip–sample distance dependence of the cantilever vibration amplitude and the tip-induced surface Ga atom relaxation. In the case of a tip which reveals only As atoms as one kind of protrusion in the NC-AFM image, the damping of the cantilever vibration amplitude is small, and the frequency shift decreases gradually with decreasing tip–sample distance. On the other type of tip with which the bright and darker protrusions corresponding to both As and Ga atoms are observed, a large damping of cantilever vibration amplitude is measured with decreasing tip–sample distance. The frequency shift curve measured with this tip has a singular point. From this frequency shift curve, we conclude that the force acting between this type of tip and the sample surface is a hysteretic force. In this tip case, tip-induced surface relaxation of the topmost Ga atoms occurs. There is a relationship between the damping of the cantilever vibration amplitude and the tip-induced surface atom relaxation; that is, the energy dissipation due to the relaxation becomes remarkable.