At present the possible existence of planets around the stars of a close binary system is still matter of debate .
Can planetary bodies form in spite of the strong gravitational perturbations of the companion star ?
We study in this paper via numerical simulation the last stage of planetary formation , from embryos to terrestrial planets in the \alpha Cen system , the prototype of close binary systems .
We find that Earth class planets can grow around \alpha Cen A on a time-scale of 50 Myr .
In some of our numerical models the planets form directly in the habitable zone of the star in low eccentric orbits .
In one simulation two of the final planets are in a 2:1 mean motion resonance that , however , becomes unstable after 200 Myr .
During the formation process some planetary embryos fall into the stars possibly altering their metallicity .