An　intelligent　robust　controller,　which　combines　a　shuffled　frog-leaping　algorithm　(SFLA)　and　an　H∞　control　strategy,　is　designed　for　a　semi-active　control　system　with　magnetorheological　(MR)　dampers　to　reduce　seismic　responses　of　structures.　Generally,　the　performance　of　mixed-sensitivity　H∞　(MSH)　control　highly　depends　on　expert　experience　in　selecting　the　parameters　of　the　weighting　functions.　In　this　study,　as　a　recently-developed　heuristic　approach,　a　multi-objective　SFLA　with　constraints　is　adopted　to　search　for　the　optimal　weighting　functions.　In　the　proposed　semi-active　control,　firstly,　based　on　the　Bouc–Wen　model,　the　forward　dynamic　characteristics　of　the　MR　damper　are　investigated　through　a　series　of　tensile　and　compression　experiments.　Secondly,　the　MR　damper　inverse　model　is　developed　with　an　adaptive-network-based　fuzzy　inference　system　(ANFIS)　technique.　Finally,　the　SFLA-optimized　MSH　control　approach　integrated　with　the　ANFIS　inverse　model　is　used　to　suppress　the　structural　vibration.　The　simulation　results　for　a　three-story　building　model　equipped　with　an　MR　damper　verify　that　the　proposed　semi-active　control　method　outperforms　fuzzy　control　and　two　passive　control　methods.　Besides,　with　the　proposed　strategy,　the　changes　in　structural　parameters　and　earthquake　excitations　can　be　satisfactorily　dealt　with.　©　2017,　The　Author(s)　2017.