We present a search for the rare decays B -> h((*))nu(nu) over bar, where h((*)) stands for a light meson. A data sample of 535x10(6) B (B) over bar 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)nu(nu) over bar and B(+)-> K(+)nu(nu) over bar decays are more stringent than the previous constraints, while the first searches for B(0)-> K(0)nu(nu) over bar, pi(0)nu(nu) over bar, rho(0)nu(nu) over bar, phi nu(nu) over bar and B(+)-> K(*+)nu(nu) over bar, rho(+)nu(nu) over bar are reported.