We extend the Damour-Ruffini method and discuss Hawking radiation of Kerr-Newman-de Sitter black hole. Under the condition that the total energy and angular momentum of spacetime are conserved, taking the reaction of the radiation of particles to the spacetime into consideration and considering the interrelation between the black hole event horizon and the cosmological horizon, we obtain the black hole radiation spectrum. This radiation is no longer a strictly pure thermal spectrum. It is related to the change in Bekenstein-Hawking(B-H) entropy corresponding to black hole event horizon and the cosmological horizon. It is shown that the result satisfies the unitary principle. We also derive the correction term of B-H entropy. It leads to a new understanding of thermal radiation of the black hole.