Viscoelastic damper (VED) is one of the most effective velocity dampers, which can provide equivalent stiffness and damping for structures. The stability of the damper is an important factor affecting the control performance of dampers. However, most research works on the stability are focused on metal dampers, few research works on the stability of velocity dampers have been carried out. To solve the stability problem of VED, an energy-dissipation design method considering the stability of VED is proposed in this paper. Through parametric analysis, relationships between height-thickness ratios, loading frequency and stability-bearing capacity of VEDs are established. Then, the concepts of stability coefficient and frequency coefficient of VED are added into the mechanical model of VED. Subsequently, pseudo-dynamic tests and variable frequency loading tests are carried out for two groups of full-scale VEDs to verify the reliability of the stability coefficient and frequency coefficient. Here, a stability-based energy-dissipation design method of VEDs is proposed. Based on an actual project, nonlinear time-history analyses are carried out for the original structure and the controlled structure ignoring/considering the stability respectively. Results indicate that control effects considering stability are lower than control effects ignoring stability. In other words, it is shown that ignoring stability of VED will result in not meeting energy-dissipation expectations, which may bring potential safety hazards to the structure. Finally, to improve its stability, a new VED with improved out-of-plane stiffness is proposed. It can be concluded that it is necessary to take the VED stability into account in the design and performance evaluation of VE structures using the proposed method.