  A lattice quantum gravity model in 4 dimensional Riemannian spacetime is
constructed based on the SU(2) Ashtekar formulation of general relativity. This
model can be understood as one of the family of models sometimes called ``spin
foam models.'' A version of the action of general relativity in continuum is
introduced and its lattice version is defined. A dimensionless ``(inverse)
coupling'' constant is defined so that the value of the action of the model is
finite per lattice point. The path integral of the model is expanded in the
characters and shown to be written as a sum over surface-like excitations in
spacetime. A 3 dimensional version of the model exists and can be reduced to
lattice BF theory. The expectation values of some quantities are computed in 3
dimensions and the meanings of the results are discussed. Although the model is
studied on a hyper cubic lattice for simplicity, it can be generalized to a
randomly triangulated lattice with small modifications.
