The　normalized　algebraic　connectivity　of　a　graph　G,　denoted　by　λ2(G),　is　the　second　smallest　eigenvalue　of　its　normalized　Laplacian　matrix.　In　this　paper,　we　firstly　determine　all　trees　with　λ2(G)≥1-63.　Then　we　classify　such　trees　into　six　classes　C1,...,C6　and　prove　that　λ2(　Ti)＞λ2(Tj)　for　1≤iTi∈Ci　and　Tj∈Cj.　At　the　same　time,　the　values　of　the　normalized　algebraic　connectivity　for　the　six　classes　of　trees　are　provided,　respectively.　These　results　are　similar　to　those　on　the　algebraic　connectivity　which　were　obtained　by　Yuan　et　al.　(2008)　[8].　©　2014　Elsevier　B.V.　All　rights　reserved.