The origin of Type Ia supernova (SN Ia), namely the identity of their progenitor systems, remains unknown. The single degenerate (SD) model is considered one of the most probable candidates for SN Ia progenitors. The accretion of hydrogen-rich material on to carbon–oxygen white dwarfs (CO WDs) is crucial for understanding SN Ia from the SD model, but this process has not been well understood due to the numerical difficulties in treating H and He flashes during the accretion. For CO WD masses from 0.5 to 1.378 Msun and accretion rates in the range from 10^−8 to 10^−5 Msun/yr, we simulated the accretion of solar-composition material on to CO WDs using stellar evolution code of MESA. It's found that the super-Eddington wind is triggered at much lower accretion rates than previously thought, when the contribution of nuclear burning to the total luminosity is included. This super-Eddington wind naturally prevents the CO WDs with high accretion rates from becoming red giants. Furthermore, the super-Eddington wind works in low-metallicity environments, which may explain SNe Ia observed at high redshifts.