Supersymmetric (SUSY) extension of the Standard Model (SM) is a primary candidate for new physics beyond the SM. If SUSY breaking scale is very low, for example, the multi-TeV range, and the SUSY breaking sector, except for the Goldstino (gravitino), is decoupled from the low energy spectrum, the hidden sector effect in the minimal SUSY SM (MSSM) is well described by employing the Goldstino chiral superfield ((X)) with the nilpotent condition of ({X}^{2}=0). Although this so-called “nonlinear MSSM” (NL-MSSM) provides a variety of interesting phenomenologies, there is a cosmological problem that the lightest superpartner gravitino is too light to be the major component of the dark matter (DM) in our Universe. To solve this problem, we propose a minimal extension of the NL-MSSM by introducing a parity-odd SM singlet chiral superfield ((\Phi )). We show that the interaction of the scalar component in (\Phi ) with the MSSM Higgs doublets is induced after eliminating (F) component of the Goldstino superfield, and the lightest real scalar in (\Phi ) plays the role of the Higgs-portal DM. With a suitable choice of the model parameters, a successful Higgs-portal DM scenario can be realized. In addition, if SUSY breaking scale lies in the multi-TeV range, the SM-like Higgs boson mass of 125 GeV can be achieved by the tree-level Higgs potential through the low-scale SUSY breaking effect.