Abstract: We investigate a supersymmetric extension of the Minimal Supersymmetric Standard Model (MSSM), called the TNMSSM, containing a SU(2) Higgs triplet (Formula presented.) of Y = 0 hypercharge and a singlet superfields (Ŝ) in the corresponding superpotential. The model can be viewed, equivalently, as an extension of the NMSSM with the addition of a (Formula presented.) interaction and of an extra coupling of the triplet to the two Higgs doublets of the NMSSM. In this scenario the Higgs particle spectrum at tree-level gets additional mass contributions from the triplet and singlet scalar components respect to the MSSM, which are particularly enhanced at low tan β. We calculate the one-loop Higgs masses for the neutral physical Higgs bosons by a Coleman-Weinberg effective potential approach. In particular, we investigate separately the impact of the radiative corrections due to the electroweak, gauge-gaugino-higgsino, fermion-sfermion and Higgs self-interactions to the Higgs masses. Due to the larger number of scalars and of triplet and singlet couplings, the Higgs corrections can be larger than the strong corrections. This reduces the amount of fine-tuning required to fit the recent Higgs data. Using the expressions of the beta-functions of the model, we show that the large triplet singlet coupling remains perturbative up to ∼ 108−10 GeV. The model is also characterized by a light pseudoscalar in the spectrum, which is a linear combination of the triplet, doublet and singlet CP-odd components. We discuss the production and decay signatures of the Higgs bosons in this model, including scenarios with hidden Higgses, which could be investigated at the LHC in the current run. © 2015, The Author(s).