We investigate the properties of accretion flows onto a black hole (BH) with a mass of M BH embedded in an initially uniform gas cloud with a density of n ∞ in order to study rapid growth of BHs in the early Universe. In previous work, the conditions required for super-Eddington accretion from outside the Bondi radius were studied by assuming that radiation produced at the vicinity of the central BH has a singlepower-law spectrum ν −α at hν ≥ 13.6 eV (α ∼ 1.5). However, radiation spectra surely depends on the BH mass and accretion rate, and determine the efficiency of radiative feedback. Here, we perform two-dimensional multi-frequency radiation hydrodynamical simulations taking into account more realistic radiation spectra associated with the properties of nuclear accretion disks. We find that the critical density of gas surrounding the BH, above which a transitions to super-Eddington accretion occurs, is alleviated for a wide range of masses of seed BHs (10 M BH /M 10 6 ) because photoionization for accretion disk spectra are less efficient than those for single-power-law spectra with 1 α 3. For disk spectra, the transition to super-Eddington is more likely to occur for lower BH masses because the radiation spectra become too hard to ionize the gas. Even when accretion flows are exposed to anisotropic radiation, the effect due to radiation spectra shrinks the ionized region and likely leads to the transition to a wholly neutral accretion phase. Finally, by generalizing our simulation results, we construct a new analytical criterion required for super-Eddington accretion; (M BH /10 5 M )(n ∞ /10 4 cm −3 ) 2.4 ( /100 eV) −5/9 , where is the mean energy of ionizing radiation from the central BH.