Using the spin-polarized relativistic Korringa-Kohn-Rostoker method, we study the electronic, magnetic, and Curie temperature of Fe2−xCoxMnAl alloys. Results indicate that the Fe2−xCoxMnAl alloys preserve the ferromagnetic metallic nature, and the spin polarization is close to 80% when the Co concentration attains to 30%. The calculated total magnetic moment increases linearly as the increase of Co doping concentration, only small changes are observed for Fe(A), Mn(B), and Fe(C) atomic magnetic moments, while for the Al atom, the magnetic moment always nearly approach to zero. The Heisenberg exchange calculations imply that the Co(A)-Mn(B) exchange plays a leading role in interactions, in contrast to the Mn(B)-Mn(B) exchange in pure Fe2MnAl. We further calculate the sum of exchange coupling parameters between the constituents, and evaluate the Curie temperature of Fe2−xCoxMnAl alloys. It is found that the Mn(B)-Mn(B) and Fe/Co(A)-Mn(B) coupling parameters increase evidently with the increase of Co content, and then leading to the Curie temperature above room temperature when the Co doping concentration is over 60%, the change is also in good consistence with calculated total magnetic moment.