  In this article, we assume that there exist hidden charmed tetraquark states
with the spin-parity $J^P=1^-$, and calculate their masses with the QCD sum
rules. The numerical result indicates that the masses of the vector hidden
charmed tetraquark states are about $M_{Z}=(5.12\pm0.15) \rm{GeV}$ or
$M_{Z}=(5.16\pm0.16) \rm{GeV}$, which are inconsistent with the experimental
data on the $\pi^+ \chi_{c1}$ invariant mass distribution.
  The hidden charmed mesons $Z_1$, $Z_2$ or $Z$ may be scalar hidden charmed
tetraquark states, hadro-charmonium resonances or molecular states.
