In this work, we solved the decoupling problem of the Dirac equation with non-zero rest mass in a Kerr-Newman-De Sitter background. The physical solutions of the Dirac equation with non-zero rest mass are found outside the event horizon of Kerr-Newman-De Sitter space-time by a proper transformation. The Hawking thermal spectra formula is also dirived. The problem of the Hawking evaporation of Dirac particles in Kerr-Newman-De Sitter black hole background is thus solved.