A workpiece-gripping chuck includes a converting mechanism provided in a body, which converts a driving force from a rotary driving source into a displacement in the axial direction. First and second pistons of the converting mechanism are displaced in the axial direction under a rotary action of a pinion gear. Further, the first and second pistons are displaced in the axial direction, respectively, by supplying a pressure fluid from a first or second port formed in the body. A workpiece may be positioned by means of a pair of gripping members under the driving action of the rotary driving source, and the workpiece is further gripped by the gripping members by applying a pressing force of the pressure fluid in addition to the driving force.