  A lattice Wess-Zumino model is formulated on the basis of Ginsparg-Wilson
fermions. In perturbation theory, our formulation is equivalent to the
formulation by Fujikawa and Ishibashi and by Fujikawa. Our formulation is,
however, free from a singular nature of the latter formulation due to an
additional auxiliary chiral supermultiplet on a lattice. The model posssesses
an exact $\U(1)_R$ symmetry as a supersymmetric counterpart of the L\"uscher
lattice chiral $\U(1)$ symmetry. A restration of the supersymmetric
Ward-Takahashi identity in the continuum limit is analyzed in renormalized
perturbation theory. In the one-loop level, a supersymmetric continuum limit is
ensured by suitably adjusting a coefficient of a single local term $\tilde
F^*\tilde F$. The non-renormalization theorem holds to this order of
perturbation theory. In higher orders, on the other hand, coefficents of local
terms with dimension $\leq4$ that are consistent with the $\U(1)_R$ symmetry
have to be adjusted for a supersymmetric continuum limit. The origin of this
complexicity in higher-order loops is clarified on the basis of the Reisz power
counting theorem. Therefore, from a view point of supersymmetry, the present
formulation is not quite better than a lattice Wess-Zumino model formulated by
using Wilson fermions, although a number of coefficients which require
adjustment is much less due to the exact $\U(1)_R$ symmetry. We also comment on
an exact non-linear fermionic symmetry which corresponds to the one studied by
Bonini and Feo; an existence of this exact symmetry itself does not imply a
restoration of supersymmetry in the continuum limit without any adjustment of
parameters.
