  We consider the exclusive flavor changing neutral current processes B -> M
\nu \bar{\nu} (M= \pi, K, \rho, K^*) in the leptophobic Z^\prime model, in
which the charged leptons do not couple to the extra Z^\prime boson. We find
that these exclusive modes are very effective to constrain the leptophobic
Z^\prime model. In the leptophobic Z^\prime model, additional right-handed
neutrinos are introduced and they can contribute to the missing energy signal
in B -> M + E_missing decays. Through the explicit calculations, we obtain
quite stringent bounds on the model parameters, |U_{sb}^{Z^\prime}| \leq 0.29
and |U_{db}^{Z^\prime}| \leq 0.61, from the already existing experimental data.
We also briefly discuss an interesting subject of massive right-handed
neutrinos, which might be connected with the dark matter problem.
