The Atacama Millimeter/Sub-millimeter Array (ALMA) is one of the most powerful telescopes built to date. All the receivers that cover the 10 frequency bands (35–950 GHz) in ALMA must comply with stringent requirements in order to perform astronomical observations, in particular, low noise temperature and high aperture efficiency. The ALMA band 1 receiver optics (35–52 GHz) are composed of a corrugated horn antenna and a dielectric lens. They have proved difficult to design because of the large bandwidth to cover and truncation effects in cryostat apertures. This paper presents a design which meets the stringent ALMA requirements.