We study the axial model in a background gravitational field. Using the ζ-function regularization, we obtain explicity the anomalous divergence of the axial-vector current and the exact generating functional of the theory. We show that, as a consequence of a space-time-dependent metric, all differential equations involved in the theory generalize to their covariantized forms. We also comment on the finitemass renormalization exhibited by the pseudoscalar field and the form of the fermion propagator.