Vibration signals of rotating machinery driven by the variable-frequency converter have the characteristics of complex modulation components, wide frequency bands involved, and serious noise interference. It is difficult to extract the mono-component modulation components related to faults. To address these issues, a new variational nonlinear single chirp mode extraction (VNSCME) method is proposed, which formulates a variational optimization model with the combination constraints of the narrowest demodulation frequency band of a single target mode and the minimum energy of the residual component. A specific mono-component nonlinear modulation component is extracted by iteration. By being preset a priori knowledge about the instantaneous frequency of the target mode, VNSCME can independently extract the specific mono-component modulation component and accurately estimate its instantaneous frequency. Compared with the existing researches, VNSCME has advantages of without the resolution limitation of time-frequency distribution, simple initialization and high computational efficiency. The combination of VNSCME and order tracking is applied to the bearing fault diagnosis of the motor driven by variable-frequency converter. The simulated and measured fault vibration signals are processed respectively, and the results indicate that the relative error of instantaneous rotating frequency estimation is less than 0. 76% , and the calculation time for extracting a single target mode is less than 11. 9 s, verifying the effectiveness of the proposed method.