  Blazar variability may be driven by stochastic processes. On the other hand,
quasi-periodic oscillation (QPO) behaviors are recently reported to be detected
in $\it{Fermi}$-LAT data of blazars. However, the significances of these QPO
signals given by traditional Fourier-like methods are still questioned. We
analyze $\gamma$-ray light curves of the QPO blazars with two Gaussian process
methods, CARMA and $\it{celerite}$, to examine the appropriateness of Gaussian
processes for characterizing $\gamma$-ray light curves of blazars and the
existence of the reported QPOs. We collect a sample of 27 blazars with possible
$\gamma$-ray periodicity and generate their $\sim11$ years $\it{Fermi}$-LAT
light curves. We apply the Gaussian process models to the $\gamma$-ray light
curves, and build their intrinsic power spectral densities (PSDs). The results
show that in general the $\gamma$-ray light curves can be characterized by
CARMA and $\textit{celerite}$ models, indicating that $\gamma$-ray
variabilities of blazars are essentially Gaussian processes. The resulting PSDs
are generally the red noise shapes with slopes between $-0.6$ and $-1.7$.
Possible evidence for the $\gamma$-ray QPOs in PKS 0537$-$441 and PG 1553$+$113
are found in the Gaussian process modelings.
