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The femtosecond laser filamentation is of significant interest due to its remarkable characteristics, and determining the critical power of self-focusing is essential for the process of filamentation. In this work, the critical power for self-focusing of intense femtosecond laser pulses at different repetition rates is experimentally measured according to the focus-shift method. A bimodal fitting method is proposed to more accurately determine the self-focusing critical power. It is found that the self-focusing critical power decreases as the laser repetition rate increases. A numerical simulation of the filamentation process based on the modified nonlinear Schrödinger equation effectively explains the experimental results obtained. This work provides valuable insights for the generation and application of high repetition rate femtosecond laser filamentation.