The eccentricity is one of the most common trouble sources in electrical machines. The angular eccentricity in which case the unequal air-gap length is related to the axial coordinate was rarely studied. This paper aims to investigate the vibration characteristics of an eccentric rotor with both the radial and angular eccentricity in the three-dimensional space. The air-gap length of eccentric rotor is derived and the electromagnetic excitation which consists of the electromagnetic force and torque is obtained. The gyroscopic effect is taken into consideration and the dynamic equations of the rotor system with four degrees of freedom are established. The electromagnetic excitation, static angular misalignment are investigated for their effects on the dynamic response in both the time domain and frequency domain, respectively. Simulation results illustrate that the electromagnetic excitation cannot be ignored in the dynamic model. The axially inclined angle determines the vibration amplitude, while the mean of steady response depends on the orientation angle.