  We analyze the quasi-periodic oscillation (QPO) of the historical light curve
of FSRQs PKS 0405-385 detected by the Fermi LAT from August 2008 to November
2021. To identify and determine the QPO signal of PKS 0405-385 in the
$\gamma$-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 quasi-periodic behavior of $\sim$2.8 yr
with the significance of $\sim$4.3$\sigma$ in Fermi long-term monitoring.
Remarkably, we also performed QPO analysis in the G-band light curve observed
from October 2014 to October 2021 using LSP and WWZ technology, and the results
($\sim$4$\sigma$ of significance) are consistent with the periodic detection in
$\gamma$-ray. This may imply that the optical emission is radiated by an
electron population same as the \gr\ emission. In discussing the possible
mechanism of quasi-periodic 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.
