PURPOSE: To obtain a special conjugate fiber giving mild luster, deep color tone or mottle effect by producing a sheath-core conjugate fiber composed of a fiber-forming polymer as core component and a specific mixed polymer as sheath component and removing a part of the sheath component of the conjugate fiber with an alkali.

CONSTITUTION: The objective special conjugate fiber having mild luster and arbitrarily controllable feeling and touch can be produced by providing a sheath- core conjugate fiber consisting of a core component composed of a fiber-forming polymer (preferable example; polyethylene terephthalate) and a sheath component composed of a polymer mixture of polyethylene terephthalate and a polymer produced by compolymerizing 3-4.5mol% of 5-sulfoisophthalic acid salt and 8-10wt.% of polyethylene glycol having a molecular weight of 5,000 to polyethylene terephthalate, and removing the sheath component with an alkaline solution, thereby exposing a part of the core component on the fiber surface.