A single crystal of the Fe-6 at% Co-15 at% Ga ternary alloy was successfully grown by the Czochralski method. The as-grown ingot with the <100> orientation parallel to the pull-up direction was about 17 mm in maximum diameter and about 55 mm in length. The magnetostriction constant in the <100> orientation λ 100 of the single crystal specimen was about 113 ppm. This value is smaller than that of an Fe-Ga alloy single crystal with the same Ga concentration, which has been grown by the Bridgman method and subsequent heat treatment. In addition, the Young's modulus of a grain near the <100> orientation in the as-solidified polycrystalline Fe-6% Co-18 at% Ga alloy was larger than that in the as-solidified polycrystalline Fe-Ga alloy with the same Ga concentration. Consequently, the partial substitution of Co for Fe in the Fe-Co alloy led to a decrease of λ 100 due to the increase of the Young's modulus in the <100> orientation.