We investigate an original domain-wall model in 4+1 dimensions numerically in the presence of U(1) dynamical gauge field only in an extra dimension, corresponding to a weak coupling limit of four-dimensional physical gauge coupling. Using a quenched approximation we carry out a numerical simulation for this model at beta(s)(= 1/g(s)(2))= 0.29 (''symmetric'' phase) and 0.5 (''broken'' phase), where g(s) is the gauge coupling constant of the extra dimension. In the broken phase, we found that there exists a critical value of a domain-wall mass m(0)(c) which separates a region with a fermionic zero mode on the domain wall from the one without it in thr same case of (2 + 1)-dimensional model. On the other hand, in the symmetric phase, our numerical data suggest that the chiral zero modes disappear in the infinite limit of four-dimensional volume. From these results it seems difficult to construct the U(1) lattice chiral gauge theory via an original domain-wall formulation.