A twin drum-type continuous casting process for casting thin cast strip by solidifying molten steel continuously fed between a pair of cooling drums placed parallel to each other, wherein the cooling drums are given an added degree of concave crown such that a solid fraction at the thickness center of the thin cast strip, when the distance from the edges toward the center of the thin cast strip at the closest position of the cooling drums is within 50 mm, is exhibited which is a value greater than the fluid critical solid fraction, or alternatively the cooling rate near the edges of the cooling drums is improved.