An accurate instantaneous speed estimation is critical in the online fault diagnosis for machines operating under varying speed condition, which is often accomplished using order tracking (OT). Tacholess order tracking (TOT) is a common employed OT technique in practical applications when the speed sensor is difficult to installed due to space or other restrictions. Applications of existing TOT is affected under the cases where the speed change is rapid or the monitored signal is contaminated by strong noise. To overcome this limitation, this paper presents a TOT method based on a Local Maximum Synchrosqueezing Transform (LMSST). Firstly, a Fast Cmspogram (FC) is deployed to determine the representative demodulation frequency band and to extract the band filtered signal correlating to a fault. LMSST is then employed to obtain the time–frequency representation (TFR) of the filtered signal where the instantaneous speed is estimated using a ridge detection algorithm based on the instantaneous frequency trajectories in the TFR. The band filtered signal is resampled at equal angular intervals according to the estimated instantaneous speed to convert the non-stationary time-domain signal into a stationary angular-domain signal. Finally, an order spectrum is obtained for the bearing fault diagnosis. The effectiveness of the method is examined using a simulated bearing defect signal and a bearing experimental data. The results show that the proposed method can produce a clear fault related order spectrum from a noise contaminated signal for an accurate bearing fault diagnosis under a strong speed varying condition.