Type la supernovae (SNe la) are believed to be thermonuclear explosions of carbon oxygen (CO) white dwarfs (WDs) with masses dose to the Chandrasekhar mass limit. How a CO WD accretes matter and grows in mass to this limit is not well understood, hindering our understanding of SN la explosions and the reliability of using SNe la as a cosmological distance indicator. In this work, we employed the stellar' evolution code MESA to simulate the accretion process of hydrogen-rich material onto a 1.0 M-circle dot CO WD at a high rate (over the Eddington limit) of 4.3 x 10(-7) M-circle dot yr(-1). The simulation demonstrates the characteristics of the double shell burning on top of the WD, with a hydrogen shell burning on top of a helium burning shell. The results show that helium shell burning is not steady (i.e. it flashes). Clashes from the helium shell are weaker than those in the case of accretion of helium-rich material onto a CO WD. The carbon to oxygen mass ratio resulting from the helium shell burning is higher than what was previously thought. Interestingly, the CO WD growing due to accretion has an outer part containing a small fraction of helium in addition to carbon and oxygen. The flashes become weaker and weaker as the accretion continues.