We present a study for two-quark light-cone distribution amplitudes for the 13D2 light tensor meson states with quantum number JPC=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 fT and fT⊥, and first Gegenbauer moment a1⊥, 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.