A semi-active friction damper (SAFD) can be employed for the seismic protection of structural systems. The effectiveness of an SAFD in absorbing seismic energy is usually superior to that of its passive counterpart, since its slip force can be altered in real time according to structural response and excitation. Most existing SAFDs are controlled by adjusting the clamping force applied on the friction interface. Thus, the implementation of SAFDs in practice requires precision control of the clamping force, which is usually substantially larger than the slip force. This may increase the implementation complexity and cost of SAFDs. To avoid this problem, this study proposes a novel position-controlled SAFD, named the leverage-type controllable friction damper (LCFD). The LCFD system combines a traditional passive friction damper and a leverage mechanism with a movable central pivot. By simply controlling the pivot position, the damping force generated by the LCFD system can be adjusted in real time. In order to verify the feasibility of the proposed SAFD, a prototype LCFD was tested by using a shaking table. The test results demonstrate that the equivalent friction force and hysteresis loop of the LCFD can be regulated by controlling the pivot position. By considering 16 ground motions with two different intensities, the adaptive feature of the LCFD for seismic structural control is further demonstrated numerically.