The copper induced green luminescence (GL) with two sets of fine structures in ZnO crystal has been found for several decades (i.e., R. Dingle, Phys. Rev. Lett. 23, 579 (1969)), but the physical origin of the doublet still remains as an open question up to now. In this paper, we provide new insight into the mechanism of the structured GL band in terms of new experimental findings and theoretical calculations. It is found, for the first time, that the GL signal exhibits persistent afterglow for tens of minutes after the switch-off of below-band-gap excitation light but it cannot occur under above-band-gap excitation. Such a phosphorous property may be interpreted as de-trapping and feeding of electrons from a shallow trapping level via the conduction band to the Cu-related luminescence centers where the Cu3+ ion is proposed to work as the final state of the GL emission. From first-principles calculation, such a Cu3+ ion in wurtzite ZnO prefers a high spin 3d8 state with two non-degenerated half-filled orbitals due to the Jahn-Teller effect, probably leading to the double structures in photoluminescence spectrum. Therefore, this model gives a comprehensively new understanding on the mechanism of the structured GL band in ZnO.