  In this article, we construct the
axialvector-diquark-scalar-diquark-antiquark type and the
axialvector-diquark-axialvector-diquark-antiquark type interpolating currents,
and study the $J^P={\frac{3}{2}}^\pm$ hidden-charm pentaquark states with the
strangeness $S=0,\,-1,\,-2,\,-3$ systematically using the QCD sum rules. The
predicted masses of the pentaquark states
$P_{uud}^{10\frac{1}{2}}\left({\frac{3}{2}^-}\right)$,
$P_{uud}^{11\frac{1}{2}}\left({\frac{3}{2}^-}\right)$ and
$P_{uud}^{11\frac{3}{2}}\left({\frac{3}{2}^-}\right)$ are compatible with the
experimental value $M_{P_c(4380)}=4380\pm 8\pm 29\,\rm{MeV}$ from the LHCb
collaboration, more experimental data are still needed to identify the
$P_c(4380)$ unambiguously.
