Micro-blog　has　become　a　symbol　of　the　novel　social　media,　and　because　of　its　rapid　development　in　such　a　short　time,　many　research　researchers　are　full　of　enthusiasm　about　it.　We　take　use　of　Latent　Dirichlet　Allocation　(LDA)　Model　which　has　excellent　dimension　reduction　capability　and　can　excavate　latent　semantic　from　texts　to　discover　popular　topics.　We　improve　the　original　LDA　model　to　FSC-LDA　model　by　combining　the　text　clustering　methods　and　feature　selection　methods,　which　can　identify　the　number　of　topics　adaptively.　FSC-LDA　model　can　keep　short　micro-blog　texts　features　better,　and　make　the　result　more　stable.　The　result　of　the　experiments　on　real　Chinese　microblog　text　dataset　shows　that　FSC-LDA　model　can　perform　well　on　the　custom　evaluation　and　find　more　accurate　popular　topics.