Magnetorheological　dampers　have　become　prominent　semi-active　control　devices　for　vibration　mitigation　of　structures　which　are　subjected　to　severe　loads.　However,　the　damping　force　cannot　be　controlled　directly　due　to　the　inherent　nonlinear　characteristics　of　the　magnetorheological　dampers.　Therefore,　for　fully　exploiting　the　capabilities　of　the　magnetorheological　dampers,　one　of　the　challenging　aspects　is　to　develop　an　accurate　inverse　model　which　can　appropriately　predict　the　input　voltage　to　control　the　damping　force.　In　this　article,　a　hybrid　modeling　strategy　combining　shuffled　frogleaping　algorithm　and　adaptive-network-based　fuzzy　inference　system　is　proposed　to　model　the　inverse　dynamic　characteristics　of　the　magnetorheological　dampers　for　improving　the　modeling　accuracy.　The　shuffled　frog-leaping　algorithm　is　employed　to　optimize　the　premise　parameters　of　the　adaptive-network-based　fuzzy　inference　system　while　the　consequent　parameters　are　tuned　by　a　least　square　estimation　method,　here　known　as　shuffled　frog-leaping　algorithm-based　adaptive-network-based　fuzzy　inference　system　approach.　To　evaluate　the　effectiveness　of　the　proposed　approach,　the　inverse　modeling　results　based　on　the　shuffled　frog-leaping　algorithm-based　adaptive-network-based　fuzzy　inference　system　approach　are　compared　with　those　based　on　the　adaptive-network-based　fuzzy　inference　system　and　genetic　algorithm-based　adaptive-network-based　fuzzy　inference　system　approaches.　Analysis　of　variance　test　is　carried　out　to　statistically　compare　the　performance　of　the　proposed　methods　and　the　results　demonstrate　that　the　shuffled　frogleaping　algorithm-based　adaptive-network-based　fuzzy　inference　system　strategy　outperforms　the　other　two　methods　in　terms　of　modeling　(training)　accuracy　and　checking　accuracy.