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文章利用判定曲面上的曲线为其测地线的充要条件，研究如何在三角域上构造以给定空间三次Bézier曲线作为其边界测地线的三次三角Bézier曲面；通过给定三次Bézier曲线的控制顶点来表示所构造的三次三角Bézier曲面的控制顶点，从而确定了所构造的曲面；讨论了具有公共边界测地线的2个三次三角Bézier曲面的连续性。为了说明所给方法的有效性，给出了几个数值实例。“,”Using the necessary and sufficient condition to determine a curve to be the geodesic curve of a surface ,this paper deals with how to construct a cubic triangular Bézier surface with a given 3D cu-bic Bézier curve as geodesic boundary in a triangular region .The explicit expression of the control points for the constructed cubic triangular Bézier surface is obtained by using the control points of the given 3D cubic Bézier curve so as to determine the required surface .In addition ,the continuity of two cubic triangular Bézier patches w hich possess common pregeodesic is discussed .Several numerical ex-amples are given to illustrate the effectiveness of the given method .