The gauge extension of the standard model with the U(1)B-L+xY symmetry predicts the existence of a light gauge boson Z'with small couplings to ordinary fermions.We discuss its contributions to the muon anomalous magnetic moment aμ.Taking account of the constraints on the relevant free parameters,we further calculate the contributions of the light gauge boson Z'to the Higgs-strahlung processes e+ e-→ ZH and e+ e-→ Z'H.