  The mass-preconditioning (MP) technique has become a standard tool to enhance
the efficiency of the hybrid Monte-Carlo simulation (HMC) of lattice QCD with
dynamical quarks, for 2-flavors QCD with degenerate quark masses, as well as
its extension to the case of one-flavor by taking the square-root of the
fermion determinant of 2-flavors with degenerate masses. However, for lattice
QCD with domain-wall fermion, the fermion determinant of any single fermion
flavor can be expressed as a functional integral with an exact pseudofermion
action $ \phi^\dagger H^{-1} \phi $, where $ H^{-1} $ is a positive-definite
Hermitian operator without taking square-root, and with the chiral structure
\cite{Chen:2014hyy}. Consequently, the mass-preconditioning for the exact
one-flavor action (EOFA) does not necessarily follow the conventional (old) MP
pattern. In this paper, we present a new mass-preconditioning for the EOFA,
which is more efficient than the old MP which we have used in Refs.
\cite{Chen:2014hyy,Chen:2014bbc}. We perform numerical tests in lattice QCD
with $ N_f = 1 $ and $ N_f = 1+1+1+1 $ optimal domain-wall quarks, with one
mass-preconditioner applied to one of the exact one-flavor actions, and we find
that the efficiency of the new MP is more than 20\% higher than that of the old
MP.
