  In the framework of BLMSSM, the Higgs decays $h^0\rightarrow Z\gamma$ and
$h^0\rightarrow m_VZ$ are studied where $m_V$ represents a vector meson($\rho,
\omega, \phi, J/\psi, \Upsilon$ etc.). Corrections to the CP-even and CP-odd
$h^0\gamma Z$ couplings occur via loop diagrams where new particles are
involved. Actually both of them obviously influence the decay rates of
$h^0\rightarrow Z\gamma$ and $h^0\rightarrow m_VZ$. Concretely, our obtained
numerical result shows that the decay width of $h^0\rightarrow Z\gamma$ can be
1.3 times larger than the prediction of the Standard Model(SM). For the light
mesons ($\rho,\omega$), the corrections to $h^0\rightarrow m_VZ$ are within
$15\%\sim 20\%$ still consistent with the SM results. The results of this work
would encourage a detection on $h^0\rightarrow Z\gamma$ at LHC for exploring
new physics beyond SM.
