  We study weak gravitational lensing of galaxy clusters in terms of the MOND
(MOdified Newtonian Dynamics) theory. We calculate shears and convergences of
background galaxies for three clusters (A1689, CL0024+1654, CL1358+6245) and
the mean profile of 42 SDSS (Sloan Digital Sky Survey) clusters and compare
them with observational data. The mass profile is modeled as a sum of X-ray
gas, galaxies and dark halo. For the shear as a function of the angular radius,
MOND predicts a shallower slope than the data irrespective of the critical
acceleration parameter $g_0$. The dark halo is necessary to explain the data
for any $g_0$ and for three interpolation functions. If the dark halo is
composed of massive neutrinos, its mass should be heavier than 2 eV. However
the constraint still depends on the dark halo model and there are systematic
uncertainties, and hence the more careful study is necessary to put a stringent
constraint.
