Abstract: In order to understand H₂⁺ harmonic emission process, by using numerical solution of non-Bohn-Oppenheimer time-dependent Schrödinger equation, high-order harmonic generation (HHG) from H₂⁺ driven by 10fs/800nm infrared (IR) field and 6fs/30nm extreme ultraviolet (XUV) pulse was theoretically investigated. The results show that, the contributions of HHG are mainly from Rabi-type oscillation, multi-photon resonance ionization, charge-resonance-enhanced ionization and dissociative ionization. With the introduction of XUV pulse, multi-harmonic cutoff extension separated by XUV photon energy can be found on HHG spectra. When the delay time between IR field and XUV pulse is larger than zero or smaller than zero, the red-shift and blue-shift of harmonics spectra can be obtained. The investigation is helpful to understand the molecular high-order harmonic generation.