We present the results of a search for the rare decays B -> h nu(nu) over bar, where h stands for K+, K-S(0), K*(+); K*(0); pi(+); pi(0), rho(+) and rho(0). The results are obtained with 772 x 10(6) B (B) over bar pairs collected with the Belle detector at the KEKB e(+)e(-) collider. We reconstruct one B meson in a semileptonic decay and require a single h meson but nothing else on the signal side. We observe no significant signal and set upper limits on the branching fractions. The limits set on the B-0 -> K-S(0)nu(nu) over bar, B-0 -> K*(0)nu(nu) over bar, B+ -> pi(+)nu(nu) over bar, B-0 -> pi(0)nu(nu) over bar, B+ -> rho(+)nu(nu) over bar, and B-0 -> rho(0)nu(nu) over bar channels are the world's most stringent.