Abstract: It is often difficult to suppress vibration of flexible rotors at high-order critical speeds through conventional low-speed balancing, especially in the case of the rotor with initial bending. In this paper, a low-speed dynamic balancing method for flexible rotors with initial bending is presented first. Combining the modal information of the rotor with the measurement data at speeds below the critical speeds, the low-speed dynamic balancing method is able to balancing the critical speeds without directly measuring the vibrations at the critical speeds and the initial bending of the rotor. Based on this, a mode-by-mode forward higher-order-extra-trial-weight-free method is proposed for balancing the higher modes simultaneously. In the proposed method, the lower-mode balancing weights on different balancing planes are used as trial weights and linked by the modal ratios of the measuring points. This avoids the potential severe vibration when pass through the critical speeds if any additional trial weights are used for balancing the higher-order modes. The proposed method is validated by numerical simulation and experimental tests respectively. The results show that the proposed method is better than the traditional influence coefficient method in balancing performance. In addition, it also avoids potentially high resonant vibration response, thus providing a safer approach for the high order dynamic balancing of flexible rotors.