This　paper　proposed　a　novel　self-centering　(SC)　rocking　column　with　the　shape　memory　alloy　slip　friction　damper　(SMASFD).　The　H-section　steel　column　was　employed　and　the　SMASFDs　which　provide　the　SC　capacity　and　dissipate　energy　were　installed　on　both　sides　of　the　column　flanges　symmetrically.　The　working　principle　and　proof-of-concept　tests　of　the　SMASFD　were　introduced　briefly　and　the　emphasis　was　put　on　the　analytical　method　of　the　cyclic　behavior　of　the　SC　rocking　column.　In　addition,　the　elaborate　finite　element　(FE)　model　of　the　SC　rocking　column　was　established　in　ABAQUS.　The　flag-shaped　hysteretic　curves　of　the　SC　rocking　column　are　obtained　from　the　analytical　method　and　FE　model,　and　a　good　agreement　can　be　found　between　them.　The　cyclic　behavior　of　the　SC　rocking　column　is　controlled　by　the　behavior　of　the　SMASFD　and　the　axial-force　ratio.　The　flexural　strength　of　the　column　will　increase　with　the　strength　of　the　SMASFD　and　increasing　the　stiffness　of　the　SMASFD　will　increase　the　stiffness　of　the　pre-yield　and　post-yield　of　the　column.　Under　the　premise　of　stabilization,　increasing　the　axial-force　ratio　will　increase　the　decompression　moment　and　the　strength　of　the　column,　however,　this　will　contribute　to　the　negative　stiffness　caused　by　the　P-Δ　effect　increase　and　amplify　the　plastic　strain　of　the　base　of　the　H-section　steel　column.　Moreover,　the　results　of　FE　models　indicate　that　the　side　plates　can　prevent　the　middle　plate　from　sliding　sideways　and　thus　the　bending　of　SMA　bolts　can　be　avoided.　©　2023　Science　Press.　All　rights　reserved.