We consider the Higgs boson mass in a class of the UMSSM models in which the MSSM gauge group is extended by an additional U(1)' group. Implementing the universal boundary condition at the GUT scale we target phenomenologically interesting regions of UMSSM where the necessary radiative contributions to the lightest CP-even Higgs boson mass are significantly small and LSP is always the lightest neutralino. We find that the smallest amount of radiative contributions to the Higgs boson mass is about 50 GeV in UMSSM, this result is much lower than that obtained in the MSSM framework, which is around 90 GeV. Additionally, we examine the Higgs boson properties in these models in order to check whether if it can behave similar to the SM Higgs boson under the current experimental constraints. We find that enforcement of smaller radiative contribution mostly restricts the U(1)' breaking scale as v(S) less than or similar to 10 TeV. Besides, such low contributions demand h(S) similar to 0.2-0.45. Because of the model dependency in realizing these radiative contributions theta(E6) < 0 are more favored, if one seeks for the solutions consistent with the current dark matter constraints. As to the mass spectrum, we find that stop and stau can be degenerated with the LSP neutralino in the range from 300 GeV to 700 GeV; however, the dark matter constraints restrict this scale as m(<(t)over tilde>), m((tau) over tilde) greater than or similar to 500 GeV. Such degenerate solutions also predict stop-neutralino and stau-neutralino co-annihilation channels, which are effective to reduce the relic abundance of neutralino down to the ranges consistent with the current dark matter observations. Finally, we discuss the effects of heavy M-Z' in the fine-tuning. Even though the radiative contributions are significantly low, the required fine-tuning can still be large. We comment about reinterpretation of the fine-tuning measure in the UMSSM framework, which can yield efficiently low results for the fine-tuning the electroweak scale. (C) 2018 The Authors. Published by Elsevier B.V.