We present an ab initio study of the magnetic surface reconstructions of the B2 FeV alloy using a self-consistent tight-binding linearized muffin tin orbital method developed in the atomic spheres approximation. For (001) and (111), the surface reconstruction stabilizes configurations unstable in the bulk alloy. When Fe is at the (001) surface, a c(222) in-plane antiferromagnetic order is found to be the ground state with magnetic moments of -2.32 µ_B and 2.27 µ_B. A p(121) O ferromagnetic order is displayed in case of V toplayer with a magnetic moment of -1.83 µ_B. At the (111) surface, we obtain for Fe toplayer two solutions p(121)N and p(221). The configuration p(121)N is found to be the ground state with a magnetic moment per atom of 2.34 µ_B. For V toplayer, only the p(121) O solution is obtained with a moment of -0.84 µ_B. In all cases, the Fe-V coupling is always antiparallel like in the bulk. Our results are discussed and compared to experiments.