  We report on our calculation of the nucleon axial and tensor charges in
2+1-flavor QCD with dynamical overlap quarks. Gauge ensembles are generated at
a single lattice spacing 0.12 fm and at a strange quark mass close to its
physical value. We employ the all-mode-averaging technique to calculate the
relevant nucleon correlation functions, and the disconnected quark loop is
efficiently calculated by using the all-to-all quark propagator. We present our
preliminary results for the isoscalar and isovector charges obtained at pion
masses $m_\pi$ = 450 and 540 MeV.
