In engineering, vibration signals of rotating machinery are nonstationary and complicated under time-varying conditions. Due to Heisenberg uncertainty principle, the traditional time-frequency analysis methods cannot extract the time-varying features accurately. In this paper, a multisynchrosqueezing transform (MSST) and frequency ridges extraction method is proposed to diagnose the rolling bearing fault with time-varying speeds. Firstly, the SST is combined with an iterative computation procedure to generate a more energy concentrated time-frequency representation. Secondly, multiple ridge curves extraction algorithm is proposed to identify the time-varying rotational frequencies and fault frequencies. Finally, the extracted frequency ridge curves are compared with theoretical fault characteristic coefficients to detect the fault types. Experimental results and comparative analysis demonstrate that the proposed method can effectively improve the resolution of time-frequency representation and extract instantaneous features.