This paper presents the precision motion control of a piezoelectric nanopositioning stage using a new scheme of adaptive sliding mode control with uncertainty and disturbance estimation (ASMC-UDE). One uniqueness of the reported ASMC-UDE scheme is that an inherent chattering-free control action is guaranteed by eliminating the use of discontinuous control term. The reported ASMC-UDE strategy is easy to realize because the hysteresis effect is not needed to be modeled. Instead, the hysteresis is estimated and compensated by the robust control scheme. The control scheme is applicable to a system plant with either matched or unmatched disturbances. Unlike the existing UDE-based SMC control schemes, a reference model is not required by the proposed ASMC-UDE scheme. The stability of the chattering-free SMC strategy is proved in theory under the Lyapunov framework. The superiority of the presented control scheme over conventional approaches has been confirmed through comparative experimental studies. Moreover, the robustness of the controller in the presence of model disturbance and external disturbance has been verified.