We analyze the quasiperiodic oscillation (QPO) of the historical light curve of flat-spectrum radio quasars PKS 0405-385 detected by the Fermi Large Area Telescope from 2008 August to 2021 November. To identify and determine the QPO signal of PKS 0405-385 in the γ-ray light curve, we use four time series analysis techniques based on frequency and time domains, i.e., the Lomb–Scargle periodogram (LSP), the weighted wavelet z-transform (WWZ), the REDFIT, and the epoch folding. The results show that PKS 0405-385 has a quasiperiodic behavior of ∼2.8 yr with the significance of ∼4.3σ in Fermi long-term monitoring. Remarkably, we also performed QPO analysis in the G-band light curve observed from 2014 October to 2021 October using LSP and WWZ technology, and the results (∼4σ of significance) are consistent with the periodic detection in γ-ray. This may imply that the optical emission is radiated by an electron population in the same way as the γ-ray emission. In discussing the possible mechanism of quasiperiodic behavior, either the helical motion within a jet or the supermassive black hole binary system provides a viable explanation for the QPO of 2.8 yr, and the relevant parameters have been estimated.