The authors have investigated magnetic properties of Ga-substituted Mn atomic wires on the GaAs(110) surface, using first-principles calculations based on the spin-density functional theory. The Mn atomic wires are assumed to align in the << 110 >>- and << 001 >>-directions. The << 110 >>-oriented wire is more stable than the << 001 >>-oriented one and has the ferromagnetic ground state with the magnetic moment of 4.0 mu(B) per Mn atom. The band structure has a large dispersion along the wire and exhibits a half-metallic state. The ferromagnetic character of the Mn wire results from the double exchange interaction through the p-d hybridization between the Mn-3d and the GaAs surface states.