  The weak lensing (WL) distortions of distant galaxy images are sensitive to
neutrino masses by probing the suppression effect on clustering strengths of
total matter in large-scale structure. We use the latest measurement of WL
correlations, the CFHTLS data, to explore constraints on neutrino masses. We
find that, while the WL data alone cannot place a stringent limit on neutrino
masses due to parameter degeneracies, the constraint can be significantly
improved when combined with other cosmological probes, the WMAP 5-year (WMAP5)
data and the distance measurements of type-Ia supernovae (SNe) and baryon
acoustic oscillations (BAO). The upper bounds on the sum of neutrino masses are
m_tot = 1.1, 0.76 and 0.54 eV (95% CL) for WL+WMAP5, WMAP5+SNe+BAO, and
WL+WMAP5+SNe+BAO, respectively, assuming a flat LCDM model with finite-mass
neutrinos. In deriving these constraints, our analysis includes the
non-Gaussian covariances of the WL correlation functions to properly take into
account significant correlations between different angles.
