  We study the effect of sigma meson on the $D_1(2430) \to D\pi\pi$ decay by
constructing an effective Lagrangian preserving the chiral symmetry and the
heavy quark symmetry. The sigma meson is included through a linear sigma model,
in which both the $q\bar{q}$ and $qq\bar{q}\bar{q}$ states are incorporated
respecting their different $U(1)_{A}$ transformation properties. We first fit
the sigma meson mass and $\sigma$-$\pi$-$\pi$ coupling constant to the I=0,
$S$-wave $\pi$-$\pi$ scattering data. Then, we show how the differential decay
width $d\Gamma(D_1 \to D(\pi\pi)_{I = 0, L =0})/d m_{\pi\pi}$ depends on the
quark structure of the sigma meson. We find that our study, combing with the
future data, can give a clue to understand the sigma meson structure.
