Due　to　the　usage　habits,　it　is　challenging　to　conduct　the　complete　process　of　lithium-ion　batteries　(LIBs)　from　fully　discharged　to　the　maximum　charge　in　real　situations.　To　achieve　battery　accuracy　state-of-health　(SOH)　estimation　in　random　charging　situations,　this　study　proposes　a　novel　health　feature　extraction　strategy　based　on　random　charging　curve　fitting　and　an　enhanced　broad　learning　system　(BLS).　First,　a　multi-objective　particle　swarm　optimization　(MOPSO)　algorithm　is　utilized　to　determine　the　optimal　voltage　interval　for　data　extraction.　Second,　the　random　charging　curve　segments　are　fitted　by　a　quadratic　function　to　characterize　health　features　(HFs).　Finally,　this　study　proposes　a　battery　SOH　estimation　model,　i.e.,　the　attention　mechanism-based　BLS　(ABLS).　The　attention　mechanism　reduces　the　uncertainty　caused　by　the　random　weights　of　the　BLS　for　the　inputs.　A　dropout　layer　is　incorporated　into　the　BLS　model　to　mitigate　the　risk　of　overfitting.　Experiments　are　conducted　on　the　NASA,　Oxford,　and　Michigan　datasets,　with　most　estimation　errors　below　1　%.　Experimental　results　demonstrate　that　the　proposed　method　has　the　potential　for　implementation　in　practical　situations　involving　LIBs.　Furthermore,　the　estimation　efficacy　of　the　battery　SOH　is　both　reliable　and　accurate.