Super-Eddington accretion is very efficient in growing the mass of a black hole: in a fraction of the Eddington time its mass can grow to an arbitrary large value if the feedback effect is not taken into account. However, since super-Eddington accretion has a very low radiation efficiency, people have argued against it as a major process for the growth of the black holes in quasars since observations have constrained the average accretion efficiency of the black holes in quasars to be >rsim0.1. In this paper, we show that the observational constraint does not need to be violated if the black holes in quasars have undergone a two-phase growing process: with a short super-Eddington accretion process they get their masses inflated by a very large factor until the feedback process becomes important, then with a prolonged sub-Eddington accretion process they have their masses increased by a factor of >rsim 2. The overall average efficiency of this two-phase process is then >rsim 0.1, and the existence of black holes of masses ∼109 M⊙ by redshift 6 is easily explained. An observational test of the existence of the super-Eddington accretion phase is briefly discussed.