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The double star S(n, m), where n⩾ m⩾ 0, is the graph consisting of the union of two stars K1,nand K1,mtogether with a line joining their centers. Its ramsey number r(S(n, m)) is the least number psuch that there is a monochromatic copy of S(n, m) in any 2-coloring of the edges of Kp. It is shown that r(S(n, m)) = max(2n+ 1, n+ 2m+ 2) if nis odd and m⩽2 and r(S(n, m)) = max(2n+ 2, n+ 2m+ 2) otherwise, for n⩽ √2morn⩾ 3m.