We　present　an　alternative　scheme　to　achieve　Schrödinger　cat　states　in　a　strong　coupling　hybrid　cavity　optomechanical　system.　Under　the　single-photon　strong-coupling　regime,　the　interaction　between　the　atom–cavity–oscillator　system　can　induce　the　mesoscopic　mechanical　oscillator　to　Schrödinger　cat　states.　Comparing　to　previous　schemes,　the　proposed　proposal　consider　the　second　order　approximation　on　the　Lamb–Dicke　parameter,　which　is　more　universal　in　the　experiment.　Numerical　simulations　confirm　the　validity　of　our　derivation.　©　2022　by　the　authors.