  We study the SM-like Higgs boson decays $h\rightarrow MZ$ in the Triplet
extended NMSSM (TNMSSM),where M is a vector meson ($\rho$, $\omega$, $\phi$,
$J/\Psi$, $\Upsilon$). Compared to the minimal supersymmetric standard model
(MSSM), the TNMSSM includes two new SU(2) triplets with hypercharge $\pm 1$ and
a SM gauge singlet which are coupled to each other. The indirect contributions
to the decays $h \rightarrow MZ$ are produced from the effective $h\gamma Z$
vertex, and they are more important than the direct contributions. The results
of this work would encourage a detection on $h \rightarrow Z\gamma$ at the
future high energy colliders for exploring new physics beyond the SM.
