We investigate high-order harmonic generation (HHG) of Li+ion driven by an intense infrared (IR) laser field in com-bination with a weak XUV pulse. To achieve this, we first construct an accurate single-active electron angular-momentum-dependent model potential of Li+ion, by which the accurate singlet energy levels of Li+for the ground state and excited states with higher quantum numbers can be obtained. Then, we solve numerically the three dimensional time-dependent Schr?dinger equation of Li+ion by means of the generalized pseudospectral method to obtain HHG. Our results show that the strength of assisted XUV is not amplified during the harmonic generation process, but the yield of HHG power spectrum in the whole plateau has a significant enhancement. Furthermore, the optimal phase delay between the IR and XUV pulses allows the production of ultrabroadband supercontinuum spectra. By superposing some harmonics, a strong new single 27-attosecond ultrashort pulse can be obtained.