In this paper, we have extended the Hawking evaporation of Dirac particles in extreme Kerr and Kerr-Newman black hole background to the case of general Kerr-Newman black hole. The physical solutions of the Dirac equation with non-zero rest mass are found outside the event horizon of a general Kerr-Newman black hole by a proper transformation. The Hawking thermal spectra formula is also derived. The problem of the Hawking evaporation of Dirac particles in general Kerr-Newman black hole background have been solved, (ref. 6).