Atomic force microscopy (AFM) based nanomanipulations have been successfully applied to various fields such as physics, material science and biomedical studies. In general, the precision of AFM based nanomanipulation has been compromised mainly by hysteresis and creep of the piezo actuator. In this paper, a new approach, named scan range adaptive hysteresis/creep hybrid (SAH) compensator, is proposed to compensate the nonlinear rate-independent hysteresis and linear rate-dependent creep effects of the open-loop AFM based manipulation system. The nonlinear portion of the SAH compensator consists of Prandtl-Ishlinskii (PI) play operators and the linear portion, which serves as an input amplifier, consists of creep operators. The advantage of the SAH compensator is that the hysteresis compensator portion can optimize its parameters to adapt to the manipulation range, which guarantees the same level of relative positioning accuracy in different operation scales. This SAH compensator is easy to implement in a range of scanning probe microscopies (SPMs). Experimental results show that the SAH compensator can compensate hysteresis and creep with higher accuracy than the conventional creep/hysteresis hybrid compensator in different operation scales.