We present the classical solution of Lagrange equations for the Reissner-Nordstrom black hole with a global monopole in the background of de Sitter space-time. Then we obtain the wavefunction of the space-time by solving the Wheeler-De Witt equation. De Broglie-Bohm interpretation applied to the wavefunction gives the quantum solution of the space-time. Finally, the quantum effect on Hawking radiation is studied.