Hawking radiation of NUT-Kerr-Newman de Sitter black hole is studied via anomalous point of view in this paper. The results show that the charged current and energymomentum tensor fluxes, to restore gauge invariance and general coordinate covariance at the quantum level in the effective field theory, are exactly equal to those of Hawking radiation from the event horizon (EH) and the cosmological horizon (CH) of NUT-Kerr-Newman de Sitter black hole, respectively.