•A new asymmetrical viscous damper (AVD) and asymmetrical dashpot (AD) model are proposed.•Setting AVD in parallel with tension-only brace (TOB) forms a TOB-AVD damping system.•The TOB-AVD decouples the damping and stiffness of the device.•The TOB-AVD dissipates seismic energy and eliminates the degradation phenomenon in the tension-only braced structures. The stiffness and damping force are coupled in traditional damping devices for tension-only braced structures resulting in insufficient damping ability. A new asymmetrical viscous damper (AVD) is proposed which carries asymmetrical forces when it is tensed or compressed matching up with the tension-only brace (TOB). An uncoupled damping system of AVD setting in parallel with TOB, namely TOB-AVD is developed accordingly. The TOB-AVD can protect the tension-only braced structures from degraded slackness or straightened impulses under earthquake excitation. In this paper, an asymmetrical dashpot (AD) constitutive model is firstly proposed and implemented to the OpenSees platform. Secondly, based on combined type fluid viscous damper, two AVD samples representing the baseline and the improved one are designed, manufactured and tested. Finally, non-linear time history analysis is conducted on finite element models of a tension-only braced benchmark building with and without AVDs. The results indicate that while adopting TOB-AVD, the inter-story drift ratio, peak floor acceleration and floor acceleration amplification are reduced by 60.7%, 49.0% and 49.0% in average, eliminating the degradation phenomenon happening in TOBs and protecting both structural and non-structural components in tension-only braced structures.