Based on the Jeffcott rotor system, the gyroscopic effects caused by different disc offset installation positions in the shaft were studied, and the law of gyroscopic effect on the inherent characteristics of the rotor system and the bending vibration modes was investigated. The results from numerical calculation and comparison show that there appear obvious effects of different disc offset installation positions on the rotor system critical speed and the unbalanced response. The greater the degree of disc offset, the greater the gyroscopic effect on the critical speed and the unbalanced response. However, the gyroscopic effect can be ignored when the rotor system is completely symmetrical.