The　velocity　response　spectrum　(SV)　plays　an　important　role　in　the　seismic　design　of　structures　that　incorporate　supplementary　velocity-dependent　dampers,　which　can　be　approximated　by　the　pseudo-velocity　response　spectrum　converted　from　the　acceleration　response　spectrum　(SA).　However,　the　error　of　this　approximation　is　significant　for　short　and　long　periods.　This　paper　aims　to　develop　a　model　for　transforming　the　SA　into　the　SV.　To　systematically　explore　the　relationship　between　SA　and　SV　and　find　the　parameters　affecting　it,　a　theoretical　SA-SV　relationship　is　derived　based　on　random　vibration　theory.　Accordingly,　statistical　analyses　using　a　large　number　of　ground　motion　records　were　conducted　to　establish　a　simple　model　for　transforming　the　SA　to　the　SV.　The　results　of　the　proposed　model　are　found　to　agree　very　well　with　those　obtained　from　actual　seismic　motion　records.　This　study　promotes　the　accurate　conversion　from　SA　to　SV　and　is　particularly　useful　for　the　seismic　design　of　structures　equipped　with　velocity-dependent　dampers.　©　2024　Elsevier　Ltd