Due to high residual stress at the stiffener welds on the web, shear link dampers (SLDs) are prone to fatigue damage under cyclic loading. Therefore, a new SLD with contact-type stiffeners was designed, and cyclic loading experiments were conducted to verify its hysteretic performance. The results indicate that the web shows premature out-of-plane buckling for the SLD without stiffeners, and cracks initiate early for the SLD with conventional welded stiffeners, which are detrimental to the low-cycle fatigue performance and energy dissipation capacity. In contrast, for the SLD with contact-type stiffeners, out-of-plane buckling of the web can be effectively suppressed, and residual stresse in the web caused by stiffener welds can be avoided. Consequently, the initiation and propagation of web cracks can be delayed, which significantly improves the low-cycle fatigue performance and energy dissipation capacity of the SLD.