  The Poyakov-Nambu-Jona-Lasinio (PNJL) model was developed recently, which
includes both the chiral dynamics and (de)confinement effect and gives a good
description of lattice QCD data. In this study we use the PNJL model to
describe the quark phase, and first use it to study the evolution of
proto-neutron star (PNS) with a hadron-quark phase transition. Along the line
of a PNS evolution, we take several snapshots of PNS profiles, presenting the
fractions of different species, the equations of state (EOS), and the
mass-radius relations at different stages. The calculation shows the mixed
phase may exist during the whole evolving process, and the onset density of
quark phase decreases with the radiation of neutrinos in the heating stage. In
the cooling stage, the EOS of the mixed phase softens and the center density
increases. In this process a part of nuclear matter transforms to quark matter,
which may lead to a PNS collapsing into a black hole.
