We report the results from our analysis of 8 years of the data for the γ-ray binary LS I +61°303, obtained with the Large Area Telescope onboard the Fermi Gamma-Ray Space Telescope. We find a significant dip around the binary's periastron in the superorbital light curves, and by fitting the light curves with a sinusoidal function, clear phase shifts are obtained. The superorbital modulation seen in the binary has been long known and different scenarios have been proposed. Based on our results, we suggest that the circumstellar disk around the Be companion of this binary may have a non-axisymmetric structure, which rotates at the superorbital period of 1667 days. As a result, the density of the ambient material around the compact star of the binary changes along the binary orbit over the superorbital period, causing the phase shifts in the modulation, and around periastron, the compact star probably enters the Be disk or switches the mode of its emission due to the intereaction with the disk, causing the appearance of the dip. We discuss the implications of this possible scenario to the observed superorbital properties at multiple frequencies.