  In the Minimal Supersymmetric Standard Model (MSSM) with additional
vector-like particles (VLPs), we for the first time derive the particle mass
spectra and the Feynman rules, as well as analytically calculate the one-loop
contributions to the Higgs boson mass from the fermions and sfermions. After
discussing and numerically analysing a cases without bilinear terms and a case
with a (partial) decoupling limit, we find: (i) The corrections depend on the
mass splittings between quarks and squarks and between vector-like fermions and
their sfermions; (ii) There exists the (partial) decoupling limit, where the
VLPs decouple from the electrwoeak (EW) energy scale, even when one of the VLPs
is light around the EW scale. The reason is that the contributions to Higgs
mass can be suppressed by the (or partial) decoupling effects, which can make
the EW phenomenology very different from the MSSM; (iii) The SM-like Higgs
boson with mass around 125 GeV gives strong constraints on the VLPs if the top
squarks are around 1~TeV. Moreover, we present some numerical analyses to
understand these unique features.
