  We have searched for the decay B^+ -> omega l^+ nu in 78 fb^-1 of Y(4S) data
(85.0 million BBbar events) accumulated with the Belle detector. The final
state is fully reconstructed using the omega decay into pi^+ pi^- pi^0 and the
detector hermeticity to infer the neutrino momentum. The signal yield is
extracted by a two-dimensional fit to the lepton momentum and the invariant
p^i+ pi^- pi^0 mass. The result of the fit depends on the form factor model
assumed for the decay. Taking the average over three different models, 421 +/-
132 events are found in the data corresponding to a preliminary branching
fraction of (1.4 +/- 0.4(stat) +/- 0.2(syst) +/- 0.3(model)) * 10^-4.
