  The mechanism for producing gamma-ray quasi-periodic oscillation (QPO) in
blazar is unknown. One possibility is the geometric model, in which without the
need for intrinsic quasi-periodic variation, the relativistic Doppler factor
changes periodically, resulting in observed gamma-ray QPO. We propose a method
to test this geometric model. We analyze the {\it Fermi}-LAT data of PG
1553+113 spanning from 2008 August until 2018 February. According to 29
four-month average spectral energy distributions (SEDs) in the energy range of
0.1-300 GeV, we split the {\it Fermi}-LAT energy range into three bands: 0.1-1
GeV, 1-10 GeV, and 10-300 GeV. The spectrum in each energy range can be
successfully fitted by a power-law. The light curves and photon indices in the
three energy ranges are obtained. Then, light curves in three narrow energy
ranges, i.e., 0.2-0.5 GeV, 2-5 GeV and 20- 40 GeV, are constructed, and the
relative variability amplitudes in the three narrow energy ranges are
calculated. A discrete-correlation analysis is performed for the light curves.
Our results indicate that (i) the light curves in the different energy ranges
follow the same pattern showed in the light curve above 0.1 GeV; (ii) the three
groups of photon indices in the energy ranges of 0.1-1 GeV, 1-10 GeV, and
10-300 GeV keep nearly constant; (iii) the ratio between relative variability
amplitudes in different narrow energy ranges are equal (within their errors) to
the prediction by the Doppler effect. Our results support the scenario of the
relativistic boost producing the gamma-ray QPO for PG 1553+113.
