The Higgs sector of the U(1)-extended supersymmetric model is studied with great detail. We calculate the masses of the Higgs bosons at the one-loop level. We also calculate at the one-loop level the gluon-involving processes for the productions and decays of the scalar Higgs bosons of the model at the energy of the CERN Large Hadron Collider (LHC), where the radiative corrections due to the loops of top, bottom, and exotic quarks and their scalar partners are taken into account. We find that the exotic quark and exotic scalar quarks in the model may manifest themselves at the LHC, since the production of the heaviest scalar Higgs boson via gluon fusion processes is mediated virtually by the loops of exotic quark and exotic scalar quarks, for a reasonable parameter set of the model.