The late-time tail of massive Dirac fields in Kerr spacetime is investigated by using the black hole Green function.It is shown that in the intermediate late times there are two kinds of new properties. The one is that the asymptotic behaviour of the massive Dirac fields is dominated by a decaying tail without any oscillation, which is different from the oscillatory decaying tails of the massive scalar field; the other is that the dumping exponent for the massive Dirac field depends not only on the multiple number of the wave mode and the mass of the Dirac particle but also on the rotating parameter of the black hole.