Battery　state-of-health　(SOH)　estimation　is　an　effective　approach　to　evaluate　battery　reliability　and　reduce　maintenance　costs　for　battery-based　backup　power　supply　systems.　This　paper　proposes　a　novel　SOH　estimation　method　for　batteries,　which　only　uses　the　response　characteristics　of　load　surges　and　is,　therefore,　non-destructive　to　the　estimated　battery　and　its　system.　The　discrete　wavelet　transform　(DWT)　method　based　on　multi-resolution　analysis　(MRA)　is　used　for　wavelet　energy　features　extraction,　and　the　fuzzy　cerebellar　model　neural　network　(FCMNN)　is　introduced　to　design　the　battery　SOH　estimator.　The　response　voltage　signals　to　load　surges　are　used　in　the　training　and　detection　process　of　the　FCMNN.　Compared　to　conventional　methods,　the　proposed　method　only　exploits　characteristics　of　online　response　signals　to　the　inrush　currents　rather　than　injecting　interference　signals　into　the　battery.　The　effectiveness　of　the　proposed　method　is　validated　by　detailed　simulation　analysis　and　experiments.