New constraints are presented on the spin-dependent weakly-interacting-massive-particle-(WIMP-)nucleon interaction from the PandaX-II experiment, using a data set corresponding to a total exposure of $3.3×10^{4}kg day$. Assuming a standard axial-vector spin-dependent WIMP interaction with ${}^{129}Xe$ and ${}^{131}Xe$ nuclei, the most stringent upper limits on WIMP-neutron cross sections for WIMPs with masses above $10 GeV/c^{2}$ are set in all dark matter direct detection experiments. The minimum upper limit of $4.1×10^{-41}cm^{2}$ at 90% confidence level is obtained for a WIMP mass of $40 GeV/c^{2}$. This represents more than a factor of 2 improvement on the best available limits at this and higher masses. These improved cross-section limits provide more stringent constraints on the effective WIMP-proton and WIMP-neutron couplings.
