  A first theoretical study for neutrino-induced diffractive productions of
heavy pseudoscalar-mesons, \eta_c and \eta_b, off a nucleon is performed based
on factorization formalism in QCD. We evaluate the forward diffractive
production cross section in perturbative QCD in terms of the light-cone wave
functions of Z boson and \eta_{c,b} mesons, and the gluon distribution of the
nucleon. The diffractive production of \eta_c is governed by the axial vector
coupling of the longitudinally polarized Z boson to Q\bar{Q} pair, and the
resulting \eta_c production cross section is larger than the J/\psi one by one
order of magnitude. The bottomonium \eta_b production, which shows up for
higher beam energy, is also discussed.
