When the effects of accretion of the black hole and the Blandford- Znajek (BZ) process in active galactic nuclei are considered, the dimensionless angular momentum of the central black hole attains an equilibrium value after 10^8^ yr for the Eddington accretion. The extreme Kerr black hole will not be present in a finite time. Its presence is determined by the magnitude of the BZ effects and is independent of the mass of the central black hole. For the non-Eddington accretion, the corresponding timescale is increased by a factor of m^-1^. Using the evolution rate of accretion M_0_ is proportional to t^-γ^ derived by Padovani & Matteucei from the gas release during the evolution of stars in elliptical galaxies, the mass of the central black holes has been determined to increase more quickly, which can reach 10^10^-10^11^ M_sun_ in 10^9^ yr. This shows that the active galactic nuclei have not accreted all the available gas, even in the elliptical galaxies with little gas. A probable method for the formation of a massive black hole with a mass of 10^6^-10^9^ M_sun_ is through accretion. The formation of a massive black hole of a mass of 10^8^ M_sun_ from a small-mass initial black hole occurs at z ~ 3, which is consistent with the statistics of quasar evolution.