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In this paper, taking into account the effect of the induced interaction, we calculate the superfluid-transition temperature of ultracold Fermi gases within the framework of the non-self-consistent T-matrix approximation. The result shows that the transition temperature is reduced by about 10% at unitarity due to the induced interaction. In the Bardeen-Cooper-Schrieffer (BCS) limit, the critical temperature is about 0.45TcBCS and it is the same as the result of the usual Gorkov and Melik-Barkhudarov correction, whereas in the Bose-Einstein condensate (BEC) limit, the influence of the induced interaction can be neglected and the critical temperature turns out to be the transition temperature of ideal Bose gases. Our results show that the induced interaction cannot be neglected in the study of the BCS-BEC crossover. [ABSTRACT FROM AUTHOR]