The thesis studies the solution of Dirac equation in the non-static and spherically symmetric black hole, it change into the form of tortoise coordinate by employing the tortoise coordinate transformation. Then this changes into standard wavw equation near the event horizons and gwts Hawking radiation temperature of Dirac particles near the event horizons, which successfully obtains Hawking thermal spectrum formula. Such thermal spectrum is determined by black holes metric tensor hefts g/ 00 and g/ 01 .