  We compute the chiral condensate in 2+1-flavor QCD through the spectrum of
low-lying eigenmodes of Dirac operator. The number of eigenvalues of the Dirac
operator is evaluated using a stochastic method with an eigenvalue filtering
technique on the background gauge configurations generated by lattice QCD
simulations including the effects of dynamical up, down and strange quarks
described by the Mobius domain-wall fermion formulation. The low-lying spectrum
is related to the chiral condensate, which is one of the leading order
low-energy constants in chiral effective theory, as dictated by the
Banks-Casher relation. The spectrum shape and its dependence on the sea quark
masses calculated in numerical simulations are consistent with the expectation
from one-loop chiral perturbation theory. After taking the chiral limit as well
as the continuum limit using the data at three lattice spacings ranging
0.080-0.045 fm, we obtain $\Sigma^{1/3}$(2 GeV) = 270.0(4.9) MeV, with the
error combining those from statistical and from various sources of systematic
errors. Finite volume effect is confirmed to be under control by a direct
comparison of the results from two different volumes at the lightest available
sea quarks corresponding to 230 MeV pions.
