Rolling bearings always operate under variable speed conditions, which poses a challenge for researchers in identifying and classifying bearing faults. In contrast to the stationary speed condition, the Fault Characteristic Frequency (FCF) under variable speed conditions exhibits a variable value that depends on the instantaneous shaft rotational speed (ISRS). The representation of the FCFs in the frequency domain reveals overlapping patterns among them. To solve the mentioned problem, a novel tool is proposed and established by mixing the two methods: The Fourier-based SynchroSqueezing transform (FSST) and Principal Component Analysis (PCA). By illustrating the envelope signal in time-frequency distribution using FSST, the FCF is highlighted in each ISRS value. Finally, this time-frequency distribution is used as input of PCA to classify rolling bearings. This method successfully diagnosed both inner race fault and outer race fault of rolling bearings.