An earthquake is a natural disaster with great destructive power and the potential to cause severe damage to building structures. The rapid convergence of control systems is extremely important when a building structure suffers an earthquake. Here, an adaptive hyperbolic tangent sliding-mode control method is proposed to guarantee rapid convergence and eliminates the problem of chatter. Since seismic waves are uncertain, the proposed method combines traditional methodologies with adaptive compensation control. Simulation experiments show that the proposed method can effectively eliminate system chatter while maintaining rapid convergence, therefore effectively improving the seismic performance of the building structure.