We theoretically investigate the high-order harmonic generation of the one-dimensional hydrogen molecular ion at fixed intermediate inteuclear distance,driven by a multicycle laser field.Our results show that the initial electronic state of the hydrogen molecular ion affects the modulation of the high-order harmonic spectrum,especially the positions of the minima.Based on the two-state model,the underlying physical mechanism of the minimum is analyzed and discussed.Further analysis shows that the different positions of the minima in the different initial electronic states can be understood via the different interferences of the two phase-adiabatic states at the ionization times.