By constructing one-dimensional model potential function with variable parameters, we investigate the high order harmonic generation （HHG） of one-dimensional model hydrogen atoms and real hydrogen atom with same ground state energy in 1 cycle and 16 cycles of intense laser fields. Our results show that in the over-barrier ionization region, the intensities of HHG for one-dimensional model atoms with different potential parameters are closely related with the depth of the potential well, but independent of the Coulomb singularity of the potential.