There is a maximum for the gravity of a black hole in the vertical direction in the accretion disc. Outflows may probably be driven from the disc if the radiation flux of the disc is greater than a critical value corresponding to the maximal vertical gravity. We find that outflows are driven by the radiation force from the disc if the dimensionless mass accretion rate at the outer radiusṁ out 1 (ṁ =Ṁ /Ṁ Edd ,Ṁ is the mass accretion rate,Ṁ Edd = L Edd /0.1c 2 , and L Edd is the Eddington luminosity). Assuming the outflow to be strong to carry away sufficient gas from the disc surface, we find that the radiation of the disc is limited by such outflows. The disc luminosity, L disc /L Edd ∝ lnṁ out , at large-ṁ out cases. The Eddington ratio of the disc is ∼ 3 forṁ out ∼ 100, which is significantly lower than that of a conventional slim disc without outflows (but it is comparable with that given in Kawaguchi 2003). This implies that the emission from some ultra-luminous X-ray sources with highly super Eddington luminosity should be Doppler beamed, or intermediate mass black holes are in these sources instead of stellar mass black holes. The spectra of the discs surrounding massive black holes with outflows are saturated in the high frequency end providedṁ out 2. We suggest that the saturated emission can be observed to estimate the masses of the black holes accreting at high rates, such as the narrow-line Seyfert galaxies, with the model calculations. The rate of the mass accreted by the black hole alwaysṀ in ≃Ṁ Edd even if the mass accretion rate at the outer radiusṀ out ≫Ṁ Edd , because most of the gas is removed into the outflows by the radiation force. If this is the case, the luminous quasars at high redshifts z 6 should have grown up through persistent accretion at a rate close to the Eddington rate.