  In this paper, we analyze in detail with numerical simulations how the mask
effect can influence the weak lensing peak statistics reconstructed from the
shear measurement of background galaxies. It is found that high peak fractions
are systematically enhanced due to masks, the larger the masked area, the
higher the enhancement. In the case with about $13\%$ of the total masked area,
the fraction of peaks with SNR $\nu\ge 3$ is $\sim 11\%$ in comparison with
$\sim 7\%$ of the mask-free case in our considered cosmological model. This can
induce a large bias on cosmological studies with weak lensing peak statistics.
Even for a survey area of $9\hbox{ deg}^2$, the bias in $(\Omega_m, \sigma_8)$
is already close to $3\sigma$. It is noted that most of the affected peaks are
close to the masked regions. Therefore excluding peaks in those regions can
reduce the bias but at the expense of loosing usable survey areas. Further
investigations find that the enhancement of high peaks number can be largely
attributed to higher noise led by the fewer number of galaxies usable in the
reconstruction. Based on Fan et al. (2010), we develop a model in which we
exclude only those large masks with radius larger than $3\arcmin. For the
remained part, we treat the areas close to and away from the masked regions
separately with different noise levels. It is shown that this two-noise-level
model can account for the mask effect on peak statistics very well and the
cosmological bias is significantly reduced.
