A fixture for a piece of furniture includes at least one post, at least one mounting member, and at least one fixing unit. The post is provided with at least one fixing track which has an upper narrow portion and an inner wide portion. The fixing unit includes an abutting member secured on the fixing track, and a fastening member connected with the mounting member and the abutting member to attach the mounting member to the post. The abutting member has a width slightly smaller than the upper narrow portion of the fixing track and has a length slightly greater than the inner wide portion of the fixing track. Thus, the mounting member is located on any proper position of the fixing track by fixing of the fixing unit so that the mounting member is affixed to the post.