Unbalance faults of a rotor owing to various factors such as manufacturing imperfections, installation errors, and material inhomogeneity, cannot be avoided. Unbalance-induced vibration generally constitutes the majority of the total undesired vibrations. Thus, controlling the unbalance-induced vibration is vital to fully utilizing rotating equipment. This paper presents a novel method for solving the dynamic balancing problem of a rotor under the interference of other rotating-frequency (1X) faults. First, the vibrational behaviour of the multi-fault rotor is analysed. Thereafter, the principle for signal purification (SP) is proposed, with the aim of obtaining pure unbalance information under 1X vibration interference. Signal resampling and spectrum correction are employed to purify the signal. Finally, an SP-based suppression method for the unbalanced vibration of a rotor with multiple 1X faults is proposed. The effectiveness of the proposed method was validated by comparing its balancing effects with those of the traditional method on a rotor test platform. The experimental results demonstrated that the proposed method eliminates the unbalance fault of the rotor more thoroughly than the traditional method and maintains the effect of vibration suppression at higher speeds.