A position-fixing system for a window covering, which has a roller tube, includes a variable diameter screw, a guiding portion, and an elastic member. The variable diameter screw has a working section gradually broadening in a radial direction thereof. The guiding portion extends along an inner wall of the roller tube in an axial direction thereof. The elastic member fits around the variable diameter screw, and is movable along the guiding portion. The elastic member has a meshing portion provided on an inner side thereof to mesh with the working section, and a guided portion provided on an outer side thereof to slide along the guiding portion. When the roller tube rotates in a direction, the elastic member moves along the working section and deforms, whereby to exert a gradually increasing unit tightening force to the variable diameter screw in the radial direction, dampening its rotation.