  We re-examine the quantum geometrodynamical approach within the
Eddington-inspired-Born-Infeld theory of gravity, which was first proposed in
our previous work [1]. A thorough analysis of the classical Hamiltonian with
constraints is carried and the correctness and self-consistency of the modified
Wheeler-DeWitt equation (WDW) is studied. We find that based on the newly
obtained WDW equation derived with the use of the Dirac brackets, the
conclusion reached in Ref.[1] can be corroborated. The big rip singularity
present in the classical theory, and induced by a phantom perfect fluid, is
expected to be avoided when quantum effects encoded on the modified WDW
equation are taken into account.
