  In this article, we assume the $Z_c(4200)$ as the color octet-octet type
axial-vector molecule-like state, and construct the color octet-octet type
axial-vector current to study its mass and width with the QCD sum rules. The
numerical values $M_{Z_c(4200)}=4.19 \pm 0.08\,\rm{GeV}$ and
$\Gamma_{Z_c(4200)}\approx 334\,\rm{MeV}$ are consistent with the experimental
data $M_{Z_c(4200)} = 4196^{+31}_{-29}{}^{+17}_{-13} \,\rm{MeV}$ and
$\Gamma_{Z_c(4200)} = 370^{+70}_{-70}{}^{+70}_{-132}\,\rm{MeV}$, and support
assigning the $Z_c(4200)$ to be the color octet-octet type molecule-like state
with $J^{PC}=1^{+-}$. Furthermore, we discuss the possible assignments of the
$Z_c(3900)$, $Z_c(4200)$ and $Z(4430)$ as the diquark-antidiquark type
tetraquark states with $J^{PC}=1^{+-}$.
