A mold cooling device comprising an air feeding/discharging circuit (22) for effecting the pneumatic drive of a pump section (1) which feeds cooling liquid to a fluid flow passageway (65a) formed in a mold (64), and the feeding of air to the fluid flow passageway (65a). Let Dx be the outer diameter-equivalent dimension of the perforated raised portion (53x) of a cast article (64x), D1 be the outer diameter of the pin portion (65) of the mold (64), t1 be the outer peripheral wall-thickness of the pin portion (65), and T1 be -5.103+(0.621xDx)-(1.068xD1)+(3.61xt1). Then the time T required for feeding the cooling liquid to the fluid flow passageway (65a) after completion of the flowing of molten metal into the mold (64) is set to satisfy the relation T1 -0.5 sec.