We study a softly broken supersymmetric model whose gauge symmetry is that of the standard model gauge group times an extra Abelian symmetry U(1)'. We call this gauge-extended model the U(1)' model, and we study a U(1)' model with a secluded sector such that neutrinos acquire Dirac masses via higher-dimensional terms allowed by the U(1)' invariance. In this model the mu term of the minimal supersymmetric model (MSSM) is dynamically induced by the vacuum expectation value of a singlet scalar. In addition, the model contains exotic particles necessary for anomaly cancellation, and extra singlet bosons for achieving correct Z'/Z mass hierarchy. The neutrinos are charged under U(1)', and thus, their production and decay channels differ from those in the MSSM in strength and topology. We implement the model into standard packages and perform a detailed analysis of sneutrino production and decay at the Large Hadron Collider, for various mass scenarios, concentrating on three types of signals: (1) 0l + MET, (2) 2l + MET, and (3) 4l + MET. We compare the results with those of the MSSM whenever possible, and analyze the standard model background for each signal. The sneutrino production and decays provide clear signatures enabling distinction of the U(1)' model from the MSSM at the LHC.