  We study the D-wave c_bar s heavy meson doublets (1^-,2^-) and (2^-,3^-)
using the method of QCD sum rule in the framework of heavy quark effective
theory. Choosing the same threshold values omega_c around 2.7 Gev, we calculate
the masses of the 1^- and 3^- states. They are m_{D*_{s1}} = 2.81 \pm 0.10 GeV
and m_{D*_{s3}} = 2.85 \pm 0.08 GeV, consistent with the newly observed
D*_{s1}(2860) and D*_{s3}(2860) states by LHCb. The masses of their 2^-
partners are calculated to be 2.82 \pm 0.10 and 2.81 \pm 0.08 GeV. The mass
splittings within the same doublet are calculated to be m_{D_{s2}} -
m_{D*_{s1}} = 0.016 \pm 0.007 GeV and m_{D*_{s3}} - m_{D'_{s2}} = 0.039 \pm
0.014 GeV.
