In this work we analyzed the particle creation process of spin-1/2 particles by considering a simple cosmological model, a two-dimensional de Sitter space-time. We choose two different charts, the static and global chart, on de Sitter space-time. We solved the Dirac equation for these two charts and then used Bogoliubov coefficients to relate vacuum states in the asymptotic regions of gravitational backgrounds. By using the Bogoliubov transformation technique we compute the density of particles created. (C) 2004 Elsevier B.V. All rights reserved.