  Motivated by the similar mass splitting in light-light and heavy-light meson
system in $J^{P}=0^{-}$ and $J^{P}=0^{+}$ channel, taking into account the
operator mixing to obtain an infrared stable OPE as well as a complete both
non-perturbative and perturbative $\mathcal {O}(m_{q})$ corrections to the
correlation function, the SU(3)-symmetry breaking effects in mass splitting in
$0^{-}$ and $0^{+}$ channel of $D$ meson are analyzed by QCD sum rule approach
based on a $c\bar{q}$ underlying structure. Within the sum rule we get, taking
same threshold and Borel window for same channel, we find a correct mass
splitting tendency in both channel which agrees with observed spectrum. We find
$m_{D_{s}}-m_{D_{d}}\sim35\rm{MeV}$ in $0^{-}$ channel and
$m_{D_{d}}-m_{D_{s}}\sim12\rm{MeV}$ in $0^{+}$ channel at scale
$\mu=1\rm{GeV}$. These splitting can be accommodated with the different role of
combination of mass effects and the parity-dependent "force" induced from
non-perturbative QCD vacuum. When we scale up to $\mu=1.3\rm{GeV}$, the
splitting remains unchanged which demonstrates a correct scale invariance.
Combined with HQET, generalization to other channel of charmed meson and
$b$-system are discussed briefly also.
