  We apply the path optimization method to a QCD effective model with the
Polyakov loop at finite density to circumvent the model sign problem. The
Polyakov-loop extended Nambu--Jona-Lasinio model is employed as the typical QCD
effective model and then the hybrid Monte-Carlo method is used to perform the
path integration. To control the sign problem, the path optimization method is
used with complexification of temporal gluon fields to modify the integral path
in the complex space. We show that the average phase factor is well improved on
the modified integral-path compared with that on the original one. This
indicates that the complexification of temporal gluon fields may be enough to
control the sign problem of QCD in the path optimization method.
