We investigate a U(1) chiral gauge model in 4+1 dimensions formulated on the lattice via the domain-wall method. We calculate an effective action for smooth background gauge fields at a fermion one-loop level. From this calculation we discuss properties of the resulting four-dimensional theory, such as gauge invariance of two-point functions, gauge anomalies, and an anomaly in the fermion number current. © 1996 The American Physical Society.