CCAT-prime is a new 6 m crossed Dragone telescope designed to characterize the cosmic microwave background (CMB) polarization and foregrounds, measure the Sunyaev–Zel’dovich effects of galaxy clusters, map the [CII] emission intensity from the epoch of reionization (EoR), and monitor accretion luminosity over multiyear timescales of hundreds of protostars in the Milky Way. CCAT-prime will make observations from a 5600-m-altitude site on Cerro Chajnantor in the Atacama Desert of northern Chile. The novel optical design of the telescope combined with high-surface-accuracy (m) mirrors and the exceptional atmospheric conditions of the site will enable sensitive broadband, polarimetric, and spectroscopic surveys at sub-millimeter to millimeter wavelengths. Prime-Cam, the first light instrument for CCAT-prime, consists of a 1.8-m-diameter cryostat that can house seven individual instrument modules. Each instrument module, optimized for a specific science goal, will use state-of-the-art kinetic inductance detector (KID) arrays operated at mK and Fabry–Perot interferometers (FPI) for the EoR science. Prime-Cam will be commissioned with staged deployments to populate the seven instrument modules. The full instrument will consist of 60,000 polarimetric KIDs at a combination of 220/280/350/410 GHz, 31,000 KIDS at 250/360 GHz coupled with FPIs, and 21,000 polarimetric KIDs at 850 GHz. Prime-Cam is currently being built, and the CCAT-prime telescope is designed and under construction by Vertex Antennentechnik GmbH to achieve first light in 2021. CCAT-prime is also a potential telescope platform for the future CMB Stage IV observations.