In this paper, an inerter-based device for structural vibration control is proposed with which inertance can be altered relying on the frequency changes of the excitation. In this manner, a tuned mass damper is developed in such a way that it is assembled with a ball-screw inerter along with a new continuously variable transmission system. The device is termed an adaptive tuned mass inertance damper (ATMID). The ATMID is able to produce an alterable inertance, which gives rise to seamless variability in device frequency; consequently, the device frequency can be tuned to that of the excitation. To assess the efficiency of the device, the response amplitude of a single-degree-of-freedom harmonically induced structure controlled by the ATMID is compared with those of the passive-controlled and uncontrolled structures. Results show that in the frequency band where the effectiveness of the passive device with a mass ratio of 0.2 is degraded and even destructed, the adaptive device with a mass ratio of 0.1 and diverse inertance behaves impressively. As a result, notable oscillation suppression is obtained using the proposed adaptive device compared with passive-controlled (56%) and uncontrolled cases (21%). The presented extensive variability in the frequency of the device utilizing its transmission ratio of 0.45−2.2 leads the device to a superior level of oscillatory motion reduction in structural responses along an enlarged frequency band.