  We present a study for two-quark light-cone distribution amplitudes for the
$1^3D_2$ light tensor meson states with quantum number $J^{PC}=2^{--}$. Because
of the G-parity, the chiral-even two-quark light-cone distribution amplitudes
of this tensor meson are antisymmetric under the interchange of momentum
fractions of the quark and antiquark in the SU(3) limit, while the chiral-odd
ones are symmetric. The asymptotic leading-twist LCDAs with the strange quark
mass correction are shown. We estimate the relevant parameters, the decay
constants $f_T$ and $f_T^\perp$, and first Gegenbauer moment $a_1^\perp$, by
using the QCD sum rule method. These parameters play a central role in the
investigation of $B$ meson decaying into the $2^{--}$ tensor mesons.
