In response to the problem of rigid link of anchorage point, which occurs to spatial cable fixed on the girder and the tower of cable-stayed bridge, on the basis of tangent stiffness matrix of nonlinear spatial truss element by differential method, and according to the characteristics of the forced rigid arm without deformation but rigid motion, the relationships between the total amount and increment of the displacement and the end force of ends of rigid arms in global coordinate system were presented by treating rigid arm as the spatial vector and employing its finite rotation formula and differential method. Then, the explicit expressions of nonlinear tangent stiffness matrix of spatial stay cable 3-D truss element with rigid arms on both ends were obtained. A finite element program based on the algorithm was developed to analyze the geometric nonlinear behaviors of cable-stayed bridge. Three examples, including spatial trussed structure with or without rigid arms and a cable-stayed bridge in construction process, were employed to perform spatial geometrical nonlinear analysis. The results show that the new algorithm can solve the rigid link of anchorage point completely, and it provides a powerful tool for refined geometrical nonlinear analysis of cable-stayed bridge.