Excessive isolation-layer displacement is often encountered in base-isolated structures under strong earthquakes. Traditional energy dissipation devices are often added to control this displacement. However, the acceleration response of the superstructure is frequently amplified by these devices. An equivalent negative stiffness friction damper (ENSFD) is proposed to address this dilemma of mutually exclusive displacement and acceleration control. Frictional resistance is provided by the ENSFD only in the second and fourth quadrants of the force–displacement coordinate system. Thus, an increase in the maximum damping force of the parallel structural system is avoided. The method of slowly varying parameters was employed to derive the steady-state response equations and equivalent linearization parameters of the ENSFD system. Based on a scaled shake-table model of a high-rise shear wall structure with base isolation, a combined analysis system comprising natural rubber bearings and the ENSFD was established. The vibration control performance was evaluated using complex modal analysis and time-history analysis. According to the results, the structural period is extended by the equivalent negative-stiffness characteristics of the ENSFD. Meanwhile, displacement responses are effectively controlled by the additional damping. Sufficient accuracy for engineering analysis is exhibited by the equivalent parameters. Compared with devices providing frictional forces in all quadrants or in the first and third quadrants, superior control over isolation-layer rotation and horizontal acceleration is achieved by the ENSFD under the same additional damping level. This advantage is magnified by an increase in the structural height-to-width ratio. Furthermore, the seismic responses of short-period structures are effectively suppressed by the ENSFD. The responses of long-period structures are not amplified. Consequently, better vibration-control stability is ensured.