Turbomachinery is used widely in the energy and power industries. The configuration of the rotor system is one of the major concerns in rotating machinery. This paper describes the development of a mathematical dynamic model of the vertical Jeffcott rotor-brush seal system considering bristle interference. The effects of the main structural and operating parameters, such as the rotational speed, rotor mass, installation distance of the brush seal, and system damping, on the nonlinear dynamic behavior of the vertical system are analyzed. The bifurcation points, stability, and vibration responses of the system are investigated using axis orbits, time histories, Poincare maps, spectrum diagrams, bifurcation diagrams, and largest Lyapunov exponents. The results indicate that the amplitude of a vertical rotor system is smaller than that of a horizontal rotor system. The amplitude decreases as the installation distance and damping level increase. Reducing the rotor mass would enhances the stability of a rotor system.