In this paper, we propose a robot end-effector for fabric folding of a fabric part of a garment along a straight line. In the garment production process, some of the edges of fabric parts of a garment need to be folded before sewing. Conventional automated folding system has a fixture designed for each folding fabric part and operation. The fixture is not universal and needs to be redesigned when the shape of the folded fabric part changes. In this paper, we consider performing fabric folding without using a fixture. We propose a concept of a robot end-effector for fabric folding of a fabric part along a straight fold line and develop a prototype of an end-effector referred to as“ F-FOLD ”(Free-form FOLDing). Folding of the edge of a fabric part is achieved by moving FFOLD along the desired straight fold line. Experimental results illustrate how F-FOLD works to fold a fabric part along a straight line.