The　emergence　of　the　Free-Floating　Bike　Sharing　System　(FFBSSs)　has　brought　convenience　to　the　public　and　also　posed　new　challenges　to　urban　construction　and　management.　Inspired　by　the　ability　of　Markov　chains　to　handle　large　volumes　of　data　in　Google’s　PageRank　algorithm,　we　propose　a　Markov-chain　based　approach　to　model　the　FFBSSs　for　capturing　its　macroscopic　aggregated　properties.　The　geohash　based　algorithm　is　proposed　to　divide　a　geography　map　into　cells　due　to　the　non-stock　feature　of　the　FFBSSs.　After　this,　the　transition　matrix　of　the　Markov　chain　is　built　based　on　historical　bike　trip　data.　Spectral　clustering　properties　and　the　characteristic　that　Kemeny　constants　can　identify　the　critical　regions　are　discussed.　Then　we　use　about　3.2　million　bike　trips　real　data　of　BJUT　Beijing,　China　from　Mobike　to　demonstrate　its　application　in　identifying　clusters　and　critical　stations.　In　our　empirical　study,　three　clusters　are　identified　in　the　vicinity　of　the　BJUT,　one　of　which　is　further　analyzed　and　then　10　critical　cells　corresponding　to　the　major　sites　in　the　cluster　are　identified,　which　is　in　line　with　reality.　©　2019,　Springer　Nature　Switzerland　AG.