To overcome the shortcomings of limited application range and low precision in the existing analysis methods for sliding cable structures, a general and high-precision three-dimensional finite element method for sliding cables is proposed. Based on the catenary theory and Euler-Eytelwein equation, the governing equations of the three-dimensional sliding cable elements with known unstressed cable length and with known tensile forces are respectively developed, accounting for the thermal effect and sliding friction. The tangent stiffness matrix of the element is derived directly from the governing equations by using matrix differential. A refined analysis procedure of sliding cable structures for the whole process from tensioning to later loadings is proposed, with the capability of automatically using all types of cable elements and accurately analyzing the friction at each sliding point. The reliability and effectiveness of the proposed method are verified by three computational examples and, by the comparison with the pertinent existing theoretical solutions and, with the pertinent numerical results and experimental ones. The computational results show that the three-dimensional finite element method proposed is accurate and reliable with high computational efficiency and is very suitable for the high-precision nonlinear analysis of various sliding cable structures in engineering practice.