The CCAT-prime telescope is a 6-meter aperture, crossed-Dragone telescope, designed for millimeter and sub-millimeter wavelength observations. It will be located at an altitude of 5600 meters, just below the summit of Cerro Chajnantor in the high Atacama region of Chile. The telescope's unobscured optics deliver a field of view of almost 8 degrees over a large, flat focal plane, enabling it to accommodate current and future instrumentation fielding >100k diffraction-limited beams for wavelengths less than a millimeter. The mount is a novel design with the aluminum-tiled mirrors nested inside the telescope structure. The elevation housing has an integrated shutter that can enclose the mirrors, protecting them from inclement weather. The telescope is designed to co-host multiple instruments over its nominal 15 year lifetime. It will be operated remotely, requiring minimum maintenance and on-site activities due to the harsh working conditions on the mountain. The design utilizes nickel-iron alloy (Invar) and carbon-fiber-reinforced polymer (CFRP) materials in the mirror support structure, achieving a relatively temperature-insensitive mount. We discuss requirements, specifications, critical design elements, and the expected performance of the CCAT-prime telescope. The telescope is being built by CCAT Observatory, Inc., a corporation formed by an international partnership of universities. More information about CCAT and the CCAT-prime telescope can be found at www.ccatobservatory.org.