We have investigated a model of an accretion disk around a supermassive black hole in active galactic nuclei (AGN). Three kinds of prescription of viscosity have been examined. It is found that the distinction among the constructed models with these prescriptions is realized when the self-gravity of the disk is dominant over the central gravity in the outer region, though they yield the same consequences for the non-self-gravitating disk. The Toomre instability parameter is less than unity in the outer region, and consequently the disk becomes gravitationally unstable and is broken up into many clumps. It is also found that the appropriate condition for the density and temperature for pumping luminous H2O masers is not satisfied in our disk model. The density turns out to be rather high at a distance of the sub-parsec scale from the central black hole.