[Objective] In response to the rotor vibration issues of doubly-fed linear motor (DFLM) under AC excitation, this paper proposes an adaptive compensation control method based on the filtered-x least mean-square (FxLMS) algorithm, aimed at enhancing both the dynamic performance and the operational stability of DFLM. [Method] Firstly, the electromagnetic vibration mechanism of DFLM under AC excitation was analyzed in depth. By establishing the two-point force model of a five-phase twenty-slot DFLM under AC excitation, the generation mechanism of the pitching moment induced by AC excitation was investigated. Secondly, based on the mechanism analysis, the FxLMS algorithm was introduced as the core control method, which relied on closed-loop feedback control to adaptively inject harmonic currents, thus effectively suppressing the periodic vibration. Finally, in order to further improve the control effect, a feedforward compensation control method based on the electric angle of the mover excitation current was proposed, in combination with the above generation mechanism of electromagnetic torque, improving the dynamic response capability of the system. [Results] To validate the effectiveness of the proposed method, simulation analysis and experimental verification were conducted. A dynamic model of the DFLM was established on the Matlab/Simulink platform, and the vibration response of the mover before and after the introduction of adaptive compensation control was compared and analyzed. The simulation results indicated that the adaptive compensation control method based on the FxLMS algorithm achieved substantial suppression of vertical mover vibrations. And the introduction of feed-forward control improved the dynamic performance of the control system and reduced the regulation pressure of the feedback control. To further verify the practical performance of the algorithm, an experimental platform was set up and tests were conducted under different operating conditions. Experimental results showed that the adaptive compensation control method based on the FxLMS algorithm significantly reduced the vertical mover vibrations induced by AC excitation. [Conclusion] The adaptive compensation control method based on FxLMS algorithm utilizes the adaptive characteristics of the FxLMS algorithm, combined with the feedforward compensation strategy. This approach effectively solves the vibration problem generated during the AC excitation process of DFLM without changing the original closed-loop control structure, significantly improved the operation stability and control accuracy of DFLM. It provides a novel solution for the high-performance control of DFLM.