  We propose a practical way of circumventing the sign problem in lattice QCD
simulations with a theta-vacuum term. This method is the reweighting method for
the QCD Lagrangian after the chiral transformation. In the Lagrangian, the
P-odd mass term as a cause of the sign problem is minimized. Additionally, we
investigate theta-vacuum effects on the QCD phase diagram for the realistic 2+1
flavor system, using the three-flavor Polyakov-extended Nambu-Jona-Lasinio
(PNJL) model and the entanglement PNJL model as an extension of the PNJL model.
The theta-vacuum effects make the chiral transition sharper. We finally
investigate theta dependence of the transition temperature and compare with the
result of the pure gauge lattice simulation with imaginary theta parameter.
