In this paper, the two-component Dirac equation in Schwarzschild background space time is reduced to a one component second order equation. The effective potential and the L-S coupling term are given. Near the horizon, there is a potential wall. When K2>3η2, there is another potential well by the wall. So the particle resonating in the well will be absorbed by the horizon after penetrating through the wall. With WKB approximation, the resonance spectrum and its width are obtained. For the case of Re-issner-Nordstrom background space time, the same procedure is also carried out, and the results are discussed briefly.