  We search for $\gamma$-ray and optical periodic modulations in a distant flat
spectrum radio quasar (FSRQ) PKS 0426-380 (the redshift $z=1.1$). Using two
techniques (i.e., the maximum likelihood optimization and the exposure-weighted
aperture photometry), we obtain $\gamma$-ray light curves from \emph{Fermi}-LAT
Pass 8 data covering from 2008 August to 2016 December. We then analyze the
light curves with the Lomb-Scargle Periodogram (LSP) and the Weighted Wavelet
Z-transform (WWZ). A $\gamma$-ray quasi-periodicity with a period of 3.35 $\pm$
0.68 years is found at the significance-level of $\simeq3.6\ \sigma$. The
optical-UV flux covering from 2005 August to 2013 April provided by ASI SCIENCE
DATA CENTER is also analyzed, but no significant quasi-periodicity is found. It
should be pointed out that the result of the optical-UV data could be tentative
because of the incomplete of the data. Further long-term multiwavelength
monitoring of this FSRQ is needed to confirm its quasi-periodicity.
