Quasi-periodic eruptions (QPEs), which are a new kind of X-ray bursts with the recurrence time of several hours, have been detected from the central supermassive black holes (SMBHs) of galactic nuclei, both active and quiescent. Recently, the two newly QPEs discovered by the eROSITA show asymmetric light curves with a fast rise and a slow decline. Current models cannot explain the observational characteristics of QPEs. Here we show that QPEs can be generated from the Roche lobe overflows at each pericentre passage of an evolved star orbiting an SMBH. The evolved stars with masses of $1-10~M_odot$, which have lost Hydrogen envelopes in the post asymptotic giant branch phase, can fulfill the requirement to produce the properties of QPEs, including the fast rise and slow decay light curves, periods, energetics, and rates. Furthermore, the extreme mass ratio $sim 10^5$ between the SMBH and the companion star will produce millihertz gravitational waves, called extreme mass-ratio inspirals (EMRIs). These QPEs would be detected as EMRI sources with electromagnetic counterparts for space-based GW detectors, such as Laser Interferometer Space Antenna (LISA) and Tianqin. They would provide a new way to measure the Hubble constant and further test the so-called Hubble constant tension.
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