  We study Hawking radiation of Dirac particles with spin-$1/2$ as a tunneling
process from Schwarzschild-de Sitter and Reissner-Nordstr\"{o}m-de Sitter black
holes in background spacetimes with a spinning cosmic string and a global
monopole. Solving Dirac's equation by employing the Hamilton-Jacobi method and
WKB approximation we find the corresponding tunneling probabilities and the
Hawking temperature. Furthermore, we show that the Hawking temperature of those
black holes remains unchanged in presence of topological defects in both cases.
