Current mathematical models for analyzing the fluid-structure interaction of deepwater drilling risers are derived on the assumption that the deepwater riser system is a cylinder with a uniform cross-section. In fact, the cross-section varies from the top to the bottom of the drilling riser. Therefore, it is necessary to establish a mathematical model that considers the variation of the cross-section of the drilling riser. In the present paper, a mathematical model for the fluid-structure interaction of any variable cross-section drilling riser is established combined with a wake oscillator model. The mathematical model is solved by the generalized integral transform technique (GITT), which is a semi-analytical method with the advantages of being fast and accurate. The mathematical model and the solution method are verified against previous experimental studies. In addition, time and frequency domain analyses were carried out for a 3 000 m drilling riser system under different flow velocities. The varying cross-section will significantly change the vibration amplitude, frequency and the lock-in region of the system. Results can serve as a guide for the dynamic response prediction and the structural design of the deepwater drilling riser systems, and are of great importance for ensuring the safety operation of deepwater drilling.