A core-sheath conjugated fiber includes two kinds of polymer, wherein the core-sheath conjugated fiber is characterized in that the core component has projected shapes having projections and grooves alternately in a cross section in a direction perpendicular to the fiber axis, the projections are formed continuously in the direction of the fiber axis, and the height (H) of the projections, the width (WA) at the tip of the projections, and the width (WB) of the bottom surface satisfy the formulas at the same time: 1.0≤H/(WA)1/2≤3.0  (1) 0.7≤WB/WA≤3.0  (2).