In this study, a new higher-order Euler-Bernoulli beam element of Absolute Nodal Coordinate Formulation (ANCF) is developed for geometrically nonlinear analysis of planar structures. The strain energy of the beam element is derived by applying the definition of the Green–Lagrange strain tensor in continuum mechanics. The first contribution of this research is to realize the accurate calculation of curvature on the beam element node by additionally considering the second derivative of the position vector obtained by quintic Hermite interpolation function. Furthermore, in traditional theory, the independent variable of finite formulation is arc-length coordinate s, while in this work, a correction is come up with and proven that it is actually an equivalent parameter. Some benchmark problems of straight beams are solved by the proposed element and accurate results are obtained by just fewer elements when compared with the other works including the traditional ANCF element and B23 element of ABAQUS. What leads to this accuracy result is that the precise calculation of nodal curvature is obtained from higher order interpolation scheme. The correctness and accuracy of the proposed element are validated in this work and it can be further developed for tackling large deformation and large rotation problems of spatial curved beams.