We show in this paper that, in a U(1)-symmetric two-Higgs-doublet model, the two additional neutral Higgs bosons would become nearly degenerate in the large tanβ regime, under the combined constraints from both theoretical arguments and experimental measurements. As a consequence, the excess observed in the anomalous magnetic moment of the muon could not be addressed in the considered framework, following the usual argument where these two neutral scalars are required to manifest a large mass hierarchy. On the other hand, we find that, with an...