[Objective] Single-rotor compressors are widely used in household air-conditioners because of their compact size, high reliability and significant cost-effectiveness. However, the unbalanced centrifugal forces generated by the rotor rotation of single-rotor compressor lead to periodic load fluctuations, consequently resulting in speed ripples and associated vibration noise. These issues are particularly pronounced at low-frequency operation of the compressor. To address these issues, this paper proposes a speed ripple suppression method for compressors based on extremum seeking algorithm(ESA), aiming to enhance speed stability of the compressor under low-frequency operating conditions. [Methods] Firstly, the load characteristics of the single-rotor compressor during normal operation were analyzed. Based on this analysis, a control method was proposed to construct a feedforward compensation current based on the superimposed value of the DC component and fundamental component of the load torque. Then, the existence of extremum of motor speed fluctuation amplitude as the compensation gain and phase offset angle varied was demonstrated, and the ESA was used to dynamically adjust the amplitude and phase offset angle of the compensation current according to the speed fluctuation amplitude, so as to realize adaptive speed ripple suppression. Finally, an improved ESA based on incomplete derivative proportional integral derivative control was proposed to improve the response speed in view of the slow convergence speed problem of the traditional ESA. [Results] Using Plecs software for simulation, the results showed that in the low and medium speed or variable torque conditions, the compressor speed ripple was greatly suppressed after using the current compensation method based on the traditional ESA. The current compensation method based on the improved ESA proposed in this paper, compared with the traditional ESA, improved the convergence speed of the algorithm and optimized the dynamic performance while guaranteeing the steady state performance. [Conclusion] The speed ripple suppression method for compressors based on improved ESA proposed in this paper can achieve the optimal regulation of feedforward compensation current amplitude and phase offset angle under various operating conditions, effectively reduce the speed ripple caused by the load torque fluctuation, and provide a new perspective for optimizing compressor drive system control and integrating advanced control algorithms.