Context. Supersoft X-ray sources (SSSs) are known as possible progenitors of Type Ia supernovae. The quasi-periodic variability has been detected in the optical light curves of SSSs. However, the exact origin of such quasi-periodic observable features remains a mystery. Aims. In this paper, we aim to reproduce the observed optical quasi-periodic variability of SSSs by proposing a white dwarf (WD) accretion model with a periodic mass transfer caused by the irradiation of supersoft X-ray onto the companion star. Methods. Assuming that a periodic mass transfer from the companion star to the WD can be caused while the supersoft X-ray irradiates the companion star, we used MESA to simulate the WD accretion process and the subsequent WD evolution by adopting a periodic jagged accretion rate. Results. Comparing our results to the optical light curves of a well-observed SSS RX J0513.9-6951, we find that our models can reproduce the quasi-periodic transition between the optical high and low states of RX J0513.9-6951 because the periodic accretion rate can lead to the WD photosphere expands and contracts periodically in our models. In addition, we find that the transitional periods of the SSSs in our models strongly depend on the mass of the accreting WDs. The more massive the WD mass is, the shorter the transitional period. Conclusions. Based on our results, we suggest that the periodic mass transfer caused by the irradiation of supersoft X-ray onto the companion star may be the origin of the observed optical quasi-periodic variability in SSSs. In addition, our results indicate that the observed optical transition period of a SSS may be useful for the rough estimate of the mass of an accreting WD.