  Massive cosmic neutrinos change the structure formation history by
suppressing perturbations on small scales. Weak lensing data from galaxy
surveys probe the structure evolution and thereby can be used to constrain the
total mass of the three active neutrinos. However, much of the information is
at small scales where the dynamics are nonlinear. Traditional approaches with
second order statistics thus fail to fully extract the information in the
lensing field. In this paper, we study constraints on the neutrino mass sum
using lensing peak counts, a statistic which captures non-Gaussian information
beyond the second order. We use the ray-traced weak lensing mocks from the
Cosmological Massive Neutrino Simulations (MassiveNuS), and apply LSST-like
noise. We discuss the effects of redshift tomography, multipole cutoff
$\ell_{\rm max}$ for the power spectrum, smoothing scale for the peak counts,
and constraints from peaks of different heights. We find that combining peak
counts with the traditional lensing power spectrum can improve the constraint
on neutrino mass sum, $\Omega_m$, and $A_s$ by 39%, 32%, and 60%, respectively,
over that from the power spectrum alone.
