According to gauge invariance, elementary particles are massless. To explain masses of the particles, Higgs field is proposed and as a result of spontaneously electroweak symmetry breaking, while particles acquire their masses, the Higgs boson arises. The Higgs boson of the Standard Model(SM) is the only particle which has not been observed in experiments. The SM has also an important problem called Hierarchy Problem which is about Higgs boson mass stability. To solve this problem some theories are proposed and Supersymmetry is one of them. In this work we studied Higgs boson masses in supersymmetric models with an extra U(1) symmetry to be called U(1)? Model. We analyze the Higgs boson masses and their dependencies on various model parameters. Especially, we compute masses of all the Higgs bosons, and confront the mass of the lightest one with the LEP and Tevatron experiments. We analyze correlations among various model parameters, and also determine excluded regions by both scanning the parameter space and examining certain likely parameter values. Furthermore, we make educated projections for LHC measurements in light of the LEP and Tevatron restrictions on the parameter space.