We present a search for the rare decays B --> h(*)nunu[over ], where h(*) stands for a light meson. A data sample of 535 x 10{6} BB[over ] pairs collected with the Belle detector at the KEKB e{+}e{-} collider is used. Signal candidates are required to have an accompanying B meson fully reconstructed in a hadronic mode and signal side particles consistent with a single h(*) meson. No significant signal is observed and we set upper limits on the branching fractions at 90% confidence level. The limits on B{0} --> K{*0}nunu[over ] and B{+} --> K{+}nunu[over ] decays are more stringent than the previous constraints, while the first searches for B{0} --> K{0}nunu[over ], pi{0}nunu[over ], rho{0}nunu[over ], varphinunu[over ] and B{+} --> K{*+}nunu[over ], rho{+}nunu[over ] are reported.