Quasi-periodic eruptions (QPEs) are found in the center of five galaxies, where a tidal disruption event (TDE)-like event has been reported in GSN 069, which occurred a couple of years before the QPEs. We explain the connection of these phenomena based on a model of a highly eccentric white dwarf (WD) 104−6 M ⊙ massive black hole (MBH) binary formed by the Hill mechanism. In this system, the tidally induced internal oscillation of a WD can heat the WD envelope thereby inducing tidal nova and inflating the WD envelope, which can be captured by the MBH and form a TDE. The tidal stripping of the surviving WD in the eccentric orbit can produce QPEs. We also apply this model to the other four QPE sources. Based on the estimated fallback rate, we find that the remaining time after the QPE-observed time for these QPEs is only around 1–2 yr based on our simple model estimation, after which the WD will be fully disrupted. We also show that the accretion rate can be much higher than the Eddington accretion rate in the final stage of these QPE sources. The peak frequency of the spectral energy distribution of the disk stays in the soft X-ray band (∼0.1–1 keV), which is consistent with observational results.