  After constructing all the tetraquark interpolating currents with
$J^{PC}=1^{-+}, 1^{--}, 1^{++}$ and $1^{+-}$ in a systematic way, we
investigate the two-point correlation functions to extract the masses of the
charmonium-like states with QCD sum rule. For the $1^{--}$ $qc\bar q\bar c$
charmonium-like state, $m_X=4.6\sim4.7$ GeV, which implies a possible
tetraquark interpretation for the state Y(4660). The masses for both the
$1^{++}$ $qc\bar q\bar c$ and $sc\bar s\bar c$ charmonium-like states are
around $4.0\sim 4.2$ GeV, which are slightly above the mass of X(3872). For the
$1^{-+}$ $qc\bar q\bar c$ charmonium-like state, the extracted mass is $4.5\sim
4.7$ GeV. We also discuss the possible decay modes and experimental search of
the $1^{-+}$ charmonium-like states.
