  Properties of a scalar $\sigma$-meson are investigated in the two-flavor
Nambu-Jona-Lasinio model with the Polyakov loop. Model analysis of the phase
diagram of strong interacting matter is performed. The temperature dependence
of the $\sigma\rightarrow\pi\pi$ decay width is studied at the zero chemical
potential and near the critical end-point. The calculated strong coupling
constant $g_{\sigma\pi\pi}$ and the decay width are compared with available
experimental data and other model results. Nonthermal enhancement of the total
decay width is noted for the $\sigma$ meson near the critical end-point when
the condition $m_\sigma\geq2m_\pi$ is broken.
