  In this exploratory lattice study, low-energy near threshold scattering of
the $(\bar{D}_1 D^{*})^\pm$ meson system is analyzed using lattice QCD with
$N_f=2$ twisted mass fermion configurations. Both s-wave ($J^P=0^-$) and p-wave
($J^P=1^+$) channels are investigated. It is found that the interaction between
the two charmed mesons is attractive near the threshold in both channels. This
calculation provides some hints in the searching of resonances or bound states
around the threshold of $(\bar{D}_1 D^{*})^\pm$ system.
