The　time-varying　dynamic　characteristics　of　telescopic　cantilever　composite　laminates　were　studied　by　analytical　and　numerical　methods.　According　to　the　classical　laminate　plate　theory　and　Hamilton　principle,　a　model　of　the　telescopic　cantilever　composite　laminate　under　in-plane　excitation　and　lateral　load　was　established.　By　choosing　suitable　time-varying　modal　functions　•＞　partial　differential　equations　were　discretized　by　Galerkin　method.　The　time-varying　ordinary　differential　linear　dynamics　equation　is　obtained.　The　effect　of　axially　moving　speed　on　dynamic　characteristics　of　the　telescopic　cantilever　plate　is　studied.　The　analytical　solution　obtained　by　an　improved　multi-scale　method　and　numerical　solution　of　the　first-order　time-varying　linear　system　are　compared.　The　results　show　that　the　axial　speed　has　great　influence　on　the　dynamic　characteristics　of　the　telescopic　cantilever　plate.　Compared　with　reference　[12],　the　improved　multi-scale　method　adopted　in　this　paper　is　more　efficient　for　first-order　linear　time-varying　systems.　©　2023　Journal　of　Dynamics　and　Control.　All　rights　reserved.