  We study the ground state of the two-dimensional Anderson-Hubbard model using
a quantum real space renormalization group method. We obtain the phase diagram
near half filling. The system is always insulating with disorder. At half
filling, the system undergoes a transition from a gapless (Anderson) insulator
to an incompressible (Mott-Hubbard) insulator as the interaction $U$ reaches a
critical value $U_c$. Away from half filling, the insulating phase is always
gapless and is found to be controlled by the Anderson fixed point at half
filling. This result is similar to that obtained in the corresponding one
dimensional system and suggests strongly the importance of the
electron-electron correlation in this gapless insulating phase.
