By　using　the　method　in　[3],　several　useful　estimations　of　the　derivatives　of　the　solution　of　the　boundary　value　problem　for　a　nonlinear　ordinary　differential　equation　with　a　turning　point　are　obtained.　With　the　help　of　the　technique　in　[4],　the　uniform　convergence　on　the　small　parameter　ε　for　a　difference　scheme　is　proved.　At　the　end　of　this　paper,　a　numerical　example　is　given.　The　numerical　result　coincides　with　theoretical　analysis.　©　1990　Shanghai　University　of　Technology.