We study the effects of non-holomprphic soft SUSY-breaking terms added to the Minimal Supersymmetric Standard Model (MSSM) on the Higgs-boson masses. The calculation of the non-holomorphic contributions is perfromed at the one-loop level in the Feynman diagramatic approach. After generating a FeynArts model file with the help of SARAH, we calculate the renormalized Higgs-boson self-energies at the one-loop level using the FeynArts/FormCalc setup. The results obtained from FeynArts/FormCalc are fed to FeynHiggs to estimate the contributions to the neutral CP-even Higgs-boson masses, $M_{h,H}$, as well as to the charged Higgs-boson mass, $M_{H^{\pm}}$. For the specific set of parameter points that we choose for this study, the non-holomorphic soft-term contributions to the CP-even light Higgs boson mass $M_h$, contrary to claims in the literature, turn out to be very small. For the CP-even heavy Higgs boson mass, $M_{H}$, as well as for the charged Higgs boson mass, $M_{H^{\pm}}$, the contributions can be substantially larger for some parts of parameter space.