Abstract: This paper focuses on developing a new high precision finite element method by combining ordinary linear element and mobile node. The mobile node coupling element can change its internal field by adjusting the position of mobile node and achieve higher precision of solution with fewer elements. Because the shape function of the mobile node employs the Bezier function which is widely used in computer graphics, this coupling element is named as Bezier Coupling Element'(BCE). The element is applied to the analysis of prismatic bars under various distributed axial loads and bars of variable cross-section under concentrated axial load. Numerical results are compared with the analytical solutions and those of conventional finite element methods to verify the present method.