Adaptive Negative Stiffness Device (ANSD) has been developed recently for passive vibration control of structures. ANSD emulates negative stiffness behavior (by exerting force toward the direction of motion) to a structure, so that, the combined structure-ANSD system shows smooth elasto-plastic force-deformation behavior with virtual yielding at target (“engaging”) displacement. The device has been studied analytically and its behavior has been demonstrated experimentally in simply supported bridge model and in Single Degree of Freedom (SDOF) structure considering limited input excitations. However, efficient and cost-effective exploitation of true potential of ANSD deserves further studies. With this being the eventual goal, in this study, we explore the performances of ANSD in seismic vibration control of a tall building by implementing a nonconventional Tuned Mass Damper (TMD) with drift control. In absence of a methodology for choice of ANSD parameters in literature, reported till date, we employ a tuning criteria for nonconventional TMD, on which the drift control is imposed as a constraint, given the special significance of drifts in tall buildings. The criteria of tuning and drift control are shown to be mutually conflicting and an algorithm is presented to address the same. Simplifying assumptions are made to develop the tuning criteria in presence of nonlinearity in ANSD and P−δ nonlinearity in tall building. A Reduced Order Modeling (ROM) approach for the building-ANSD system is developed to facilitate the algorithmic computations. Robustness of our design approach is shown under an acceptable level of detuning of TMD and near fault pulse type motions. Comparative assessment with a conventional design approach is presented to show the improvements. A step by step illustration of the developed methodology is briefly touched on in context of modern performance based approach. The study is a first step toward the possible utility of ANSD in controlling seismic vulnerability of tall buildings.