Purpose　Variable　cross-section　beams　are　widely　applied　in　engineering　fields　for　their　appropriate　distribution　of　mass　and　strength.　However,　the　free-vibration　characteristics　are　difficult　to　study　by　analytical　method　because　the　governing　equation　of　the　nonuniform　beam　has　varying　flexural　stiffness　and　distributed　mass.　In　this　work,　the　asymptotic　perturbation　method　is　introduced　to　study　the　free　vibration　of　variable　width　beams.　Method　To　deal　with　the　ordinary　differential　equation　with　variable　coefficients,　based　on　the　asymptotic　perturbation　method,　the　equivalent　frequency　equation　of　the　uniform　beam　is　obtained　to　give　frequency　correction　of　the　considered　beam　structure　by　analyzing　the　first-order　terms.　The　finite-element　method　and　vibration　experiment　are　also　conducted　to　validate　the　theoretical　analysis　results.　Results　Concise　and　accurate　frequency　equations　were　derived　based　on　the　asymptotic　perturbation　method.　The　effects　of　the　width　ratio　on　the　frequencies　are　illustrated　and　discussed.　It　shows　a　good　agreement　by　comparing　the　analytical　solutions,　finite-element　analysis　results,　and　experimental　results.　In　addition,　it　is　observed　that　the　natural　frequency　reduces　with　the　increase　of　the　width　ratio.　Conclusions　The　asymptotic　perturbation　method　is　simple　and　efficient　and　can　be　used　to　conveniently　analyze　the　free　vibration　of　variable　width　beams,　moreover,　it　could　be　extended　to　analyze　the　free　vibration　of　any　other　nonuniform　beam　structures.