Let　l≥2　be　a　positive　integer　and　let　Gl　denote　the　family　of　graphs　which　have　girth　2l+1　and　have　no　holes　of　odd　length　at　least　2l+3.　Chudnovsky　and　Seymour　proved　that　every　graph　G∈G2　is　three-colorable.　In　2022,　Wu,　Xu　and　Xu　conjectured　that　every　graph　G∈⋃lGl　is　three-colorable.　Soon　after,　Wu,　Xu　and　Xu　confirmed　the　case　l=3.　In　this　note,　we　prove　that　every　graph　G∈Gl　with　radius　at　most　l+1　is　three-colorable.　This　generalizes　the　results　of　Xu,　Yu　and　Zha　in　2017.　©　2022　Elsevier　B.V.