  A light Higgs boson with substantial branching ratio into invisible channels
can occur in a variety of models with: light neutralinos, spontaneously broken
lepton number, radiatively generated neutrino masses, additional singlet
scalar(s) and/or right handed neutrinos in the extra dimensions of TeV scale
gravity. We study the observability of the WH and ZH modes at LHC with H
decaying invisibly, by carrying out a detailed simulation with two event
generators HERWIG and PYTHIA and realistic detector simulations (GETJET and
CMSJET). We find that the signal with `single lepton plus missing $E_T$'
resulting from WH production suffers from a very large background due to the
(off-shell) $W^{*}$ production via the Drell-Yan process. In contrast, the ZH
mode provides a clean signal in the `dilepton plus missing $E_T$' channel. By
exploiting this second signature, we show that invisible branching ratios of
Higgs bosons, ${BR}_{inv}$, larger than $\sim 0.42(0.70)$ can be probed at
5$\sigma$ level for $M_H = 120$(160) GeV respectively, assuming an accumulated
luminosity of L=100 fb$^{-1}$.
