Based on the physical model of a supermassive black hole (SMBH) growth via gas accretion in a circumnuclear disk (CND) proposed by Kawakatu & Wada, we describe the formation of high-z (z>6) quasars (QSOs) whose BH masses are M _BH>10⁹ M _☉. We derive the necessary conditions to form QSOs at z>6 by only gas accretion: (1) a large mass supply with M _sup>10¹⁰ M _☉from host galaxies to CNDs, because the final BH mass is only 1%-10% of the total supplied mass from QSO hosts. (2) High star formation efficiency for a rapid BH growth which is comparable to high-z starburst galaxies such as submillimeter galaxies. We also find that if the BH growth is limited by the Eddington accretion, the final BH mass is greatly suppressed when the period of mass supply from hosts, t _sup, is shorter than the Eddington timescale. Thus, the super-Eddington growth is required for the QSO formation while t _sup, which is determined by the efficiency of angular momentum transfer, is shorter than ~10⁸ yr. The evolution of the QSO luminosity depends on the redshift z _i at which accretion onto a seed BH is initiated. In other words, the brighter QSOs at z>6 favor the late growth of SMBHs (i.e., z _i 10) rather than early growth (i.e., z _i 30). For z _i 10, t _sup 10⁸ yr is shorter than that of the star formation in the CND. Thus, the gas in the CND can accrete onto a BH more efficiently, compared with the case for z _i 30 (or t _sup 10⁹ yr). Moreover, we predict the observable properties and the evolution of QSOs at z>6. In a QSO phase, there should exist a stellar rich massive CND, whose gas mass is about 10% of the dynamical mass inside ~0.1-1 kpc. On the other hand, in a phase where the BH grows (i.e., a proto-QSO phase), the proto-QSO has a gas-rich massive CND whose gas mass is comparable to the dynamical mass. Compared with the observed properties of the distant QSO SDSS J1148+5251 observed at z = 6.42, we predict that SDSS J1148+5251 corresponds to the scenario of the late growth of SMBH with z _i ~ 10, which is accompanied by a massive CNDs with M _g 5 × 10¹⁰ M _☉ and the luminous nuclear starburst L _SBat infrared band with L _SB 10⁴⁷ erg s^–1. Moreover, we predict that the progenitor of SDSS J1148+5251 can be the super-Eddington object. These predictions can be verified by ALMA, SPICA, and JWST.