We have investigated the electronic structure and magnetic properties of Fe-doped AlSb using density functional theory within the generalized gradient approximation (GGA)+U schemes. We have shown that the ground state magnetic structure of Fe-doped AlSb is antiferromagnetic. AlSbis the most plausible acceptor among several candidates for p-type conduction and the bound magnetic polarons (BMP) mechanism may be responsible for the origin of the (Al,Fe) Sb ferromagnetism.