The mechanism for producing gamma-ray quasi-periodic oscillation (QPO) in blazars 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 Fermi-LAT data of PG 1553+113 spanning from 2008 August until 2018 February. According to 29 four-month average spectral energy distributions in the energy range of 0.1-300 GeV, we split the 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; and (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.