We investigate the high-order harmonic generation (HHG) of a model atom whose initial state is prepared in a superposition of its ground state and an excited state irradiated by different duration laser pulses. Compared to the HHG generated from an atom whose initial state is in its ground state, its conversion efficiency obtains some enhancement. The enhancement originates from the higher ionization rate (rather than the ionization yield) of the atom with superposition initial state.