  We analyze the one loop correction to $Z\rightarrow \nu\nu$ decay in
framework of Minimal R-symmetric Supersymmetric Standard Model(MRSSM) in detail
with normal and inverse neutrino mass orderings, as a function of $\tan\beta$,
Dirac mass parameters $M_D^W$ and $\mu_u(\mu_d)$, slepton mass $m_l$ that
parameterize the mass matrices. The numerical results indicate that the
branching ratio for $Z\rightarrow \nu\nu$ decay is compatible with the
experimental measurement and the SM expectation at $2\sigma$ level. For inverse
neutrino mass ordering, the prediction exceeds the SM expectation at $1\sigma$
level. The prediction on $Br(Z\rightarrow \nu\nu)$ increases proportionally to
$\tan\beta$ and inversely proportionally to $m_l$. For normal neutrino mass
ordering, the peak value of the prediction on $Br(Z\rightarrow \nu\nu)$ exceeds
the SM expectation at $1\sigma$ level.
