In this paper, a sensorless control strategy of magnetic suspension centrifugal compressor (MSCC) based on an LCL filter is proposed, which can effectively suppress the interference of stator current harmonics and high dv/dt common-mode voltage on an active magnetic bearing system. First, the mathematical model of MSCC with LCL filter is established. Based on the new model, a novel terminal sliding mode extended state observer is proposed to estimate the capacitance voltage, and the stability of this method has been strictly proved by second method of Lyapunov. In addition, in order to improve the accuracy of rotor position detection, the same frequency filter compensator is designed in the static coordinate system to eliminate the phase delay and amplitude attenuation caused by the low-pass filter. Finally, the effectiveness of the proposed method is verified by simulation.