A novel all-metal vacuum bellows that can follow a twist motion around the axis was designed and developed. The bellows, called here a "twist bellows," consists of two normal bellows sections and one special bellows section whose corrugation is oblique to the axis. A trial model with a total length of 400 mm and an inner diameter of 100 mm is able to absorb the twist up to about +/-22 degrees (44 degrees total) within a twist torque of about 12 N m (120 kg cm) while keeping the total length constant. The twist bellows can also follow the usual bending, shifting, expanding and contracting motion easily like a conventional bellows. The twist bellows allows an unobstructed direct view along the axis and is especially useful for vacuum system of accelerators or synchrotron light beam lines.