<p>The multi-synchrosqueezing transform (MSST) can effectively improve the degree of concentration of time–frequency (TF) representation for analysis of signal with complicated frequency modulation. Nevertheless, the MSST strategy faces two challenges that must be addressed to improve its effectiveness. One is that predefined iteration number in MSST may not be optimal for all non-stationary signals. Another one is that even the iterative reassignment procedure with convergent number, there may still have smeared part around instantaneous frequency (IF) trajectories in the TF plot. To address these issues, this paper proposes a time-varying iteration number and frequency interval for the MSST. For the first issue, this paper makes use of the relationship between the derivative of IF and time-varying iteration number to obtain convergent number of iterative reassignment procedures for each time instant. For the second issue, with assistance of time-varying iteration number, feasible frequency interval can be achieved for each time instant by exploring the relationship between the local Rényi entropy (LRE) and frequency interval. Then, the local maximum operator based on time-varying frequency interval is applied to convergent TF representation of the MSST to squeeze smeared part into IF trajectories in the TF plot. The performance on two non-stationary signals with multi-components and two practical signals show that proposed method outperforms existing methods in the aspect of achieving sharper TF representation.</p>