Rotor systems with coupling consist of two rotors, rolling bearings, sealing components, and nonlinear coupling. Currently, rotor systems with coupling are widely used in marine engines, aerospace engines, and various vehicle engines. In studies of rotor systems with coupling, the coupling connecting both sides of the rotor are often regarded as a linear stiffness unit. But in actual engineering, the torsional stiffness of the coupling varies with the speed of the system, and the variation of the coupling stiffness will affect the dynamic characteristics of the rotor. Based on the above phenomena, this study establishes the rotor model of driveshaft-Geislinger coupling-driveshaft in diesel engines and obtains the modal, frequency, and transient response analysis results of the rotor system with nonlinear Geislinger coupling. The modal, frequency, and transient response analysis results of the nonlinear model are compared with those of the linear model. This study can provide theoretical support for the vibration analysis of nonlinear rotor systems with connected Geislinger coupling.