Base swing will bring additional gyroscopic moment and inertia load to the rotating machinery，affecting the vibration and stability of the rotor system and even endangering the rotor operation. In order to effectively control the vibration of the active magnetic bearing （AMB）-flexible rotor system under the base swing，a base acceleration feedforward algorithm is proposed in this paper. With the dynamic model and the parameters of the base swing，the optimal compensation current to suppress the vibration can be directly obtained by the proposed algorithm. Because of no iteration and simple structure，the algorithm has strong rapidity and practicality. Furtherly，to eliminate the influence of modeling error on the compensation performance，a method to correct compensating current is suggested. After that，the influence of the proposed algorithm on the rotor vibration in the spin speed range including the first bending critical speed is simulated. Finally，on the test platform，the effectiveness of the algorithm was verified when rotor in suspension without spin，constant speed and acceleration under the base swing. The theoretical and experimental results agree that the vibration perpendicular to the swing axis increases obviously due to the inertia load. The additional gyroscopic moment increases the vibration along the swing axis，and the rising amplitude grows along with the increase of the rotor spin speed. The algorithm proposed can efficiently suppress the rotor vibration under the base swing in the spin speed range including the first bending critical speed.