Underestimation and overestimation problems are commonly observed in conventional adaptive sliding mode control (ASMC). These problems refer to the fact that the adaptive controller gain unnecessarily increases when the states are approaching the sliding surface (overestimation) or improperly decreases when the states are getting far from it (underestimation). In this paper, we propose a novel ASMC strategy that overcomes such issues. In contrast to the state of the art, the proposed strategy is effective even when an a priori constant bound on the uncertainty cannot be imposed. Comparative results using a two-link manipulator demonstrate improved performance as compared to the conventional ASMC. Experimental results on a biped robot confirm the effectiveness and robustness of the proposed method under various practical uncertainties.