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Recently, some fast radio bursts (FRBs) have been reported to exhibit complex and diverse variations in Faraday rotation measurements (RM) and polarization, suggesting that dynamically evolving magnetization environments may surround them. In this paper, we investigate the Faraday conversion (FC) effect in a binary system involving an FRB source and analyze the polarization evolution of FRBs. For a strongly magnetized high-mass companion binary, when an FRB with ∼100% linear polarization passes through the radial magnetic field of the companion star, the circular polarization (CP) component will be induced and oscillate symmetrically around the point with the degree of CP equal to zero, the rate and amplitude of the oscillation decrease as the frequency increases. The very strong plasma column density in the HMCBs can cause CP to oscillate with frequency at a very drastic rate, which may lead to depolarization. Near the superior conjunction of the binary orbit, the DM varies significantly due to the dense plasma near the companion, and the significant FC also occurs in this region. As the pulsar moves away from the superior conjunction, the CP gradually tends toward zero and then returns to its value before incidence. We also investigate the effect of the rotation of the companion star. We find that a sufficiently significant RM reversal can be produced at large magnetic inclinations and the RM variation is very diverse. Finally, we apply this model to explain some polarization observations of PSR B1744-24A and FRB 20201124A. [ABSTRACT FROM AUTHOR]