Blazar variability may be driven by stochastic processes. On the other hand, quasi-periodic oscillation (QPO) behaviors were recently reported to be detected in the 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 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 similar to 11 yr 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 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.