Massless matter fields and non-Abelian gauge fields are localized on domain walls in a (4 + 1)-dimensional U(N)(c) gauge theory with SU(N)(L) x SU(N)(R) x U(1)(A) flavor symmetry. We also introduce SU(N)(L+ R) flavor gauge fields and a scalar-field-dependent gauge coupling, which provides massless non-Abelian gauge fields localized on the wall. We find a chiral Lagrangian interacting minimally with the non-Abelian gauge field together with nonlinear interactions of moduli fields as the (3 + 1)-dimensional effective field theory up to the second order of derivatives. Our result provides a step towards a realistic model building of the brane-world scenario using topological solitons.