We　say　that　a　graph　G　has　an　odd　K4-subdivision　if　some　subgraph　of　G　is　isomorphic　to　a　K4-subdivision　which　if　embedded　in　the　plane　the　boundary　of　each　of　its　faces　has　odd　length　and　is　an　induced　cycle　of　G.　For　a　number　(formula　presented),　let　Gl　denote　the　family　of　graphs　which　have　girth　2l　+　1　and　have　no　odd　hole　with　length　greater　than　(formula　presented).　Wu,　Xu　and　Xu　conjectured　that　every　graph　in　(formula　presented)fo　is　3-colorable.　Recently,　Chudnovsky　et　al.　and　Wu　et　al.,　respectively,　proved　that　every　graph　in　G2　and　G3　is　3-colorable.　In　this　paper,　we　prove　that　no　4-vertex-critical　graph　in(formula　presented)　has　an　odd　K4-subdivision.　Using　this　result,　Chen　proved　that　all　graphs　in(formula　presented)　are　3-colorable.　©　The　authors.