The problem of solving the Dirac equation in a Kerr space-time has long been unresolved. In 1976, S. Chandrasekhar solved the decoupling problem of the Dirac equation with non-zero rest mass in a Kerr background, thus provided the possibility of attacking the problem of the Hawking evaporation of Dirac particles. In this paper, starting from Chandrasekhar's results, we find the solution of the Dirac equation with non-zero rest mass just out side the event horizon of a nearly extreme Kerr black hole and sucessfully derived the Hawking thermal formula.