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.