The dual-rotor structure is susceptible to vibration, causing the malfunction of the entire operating system. In order to avoid the resonance during operation, it is significant and necessary to conduct modal analysis of such rotors. The dynamic analysis of the full dual-rotor system under operating conditions is also necessary to study dynamic characteristics of the rotating system. In this paper, one-dimension Timoshenko beam-type model, including the effects of gyroscopic moments, rotary inertias, bending and shear deformations, and three-dimension model for dual-rotor system with inter-shaft bearing are developed. Critical speed tests of dual-rotor are carried out to verify the analytical results. Based on the finite element models, the first critical speed excited by inner rotor and the first two critical speeds excited by outer rotor are calculated. The comparisons between both finite element models indicate that 1D model costs less time, which can be used to predict the critical speeds. Good agreement between the theoretical and experimental results shows the accuracy of the FE models. The Campbell diagram, critical speeds, operational deflection shapes and unbalance response of the dual-rotor are obtained to fully study the dynamic characteristics of the dual-rotor system.