Imaging the entire human cornea with a conventional OCT system configuration requires trade-offs between resolution and depth-of-focus because the cornea is curved over a depth of approximately 4 mm. These system trade-offs result in image quality variations in the corneal image such as a bright apex surrounded by decreasing intensity as the cornea curves away from the apex. These intensity changes cause non-biological ambiguities in interpreting the image, make it difficult to see anatomy in the dim areas, and make automated surface detection difficult in the periphery. To address this problem, we developed a continuously focusing corneal OCT system coupled with a constant linear velocity (CLV) spiral scan pattern that is able to better maintain focus from the apex to the deeper cornea during a scan. The continuous focusing was implemented by introducing a focusing telescope on a motorized stage into the sample arm and matching the translation of the telescope with the CLV scan as it spiraled from the corneal apex outwards. Orthogonal B-scans prior to volume acquisition were used as a reference to estimate and correct motion that occurred during the subsequent CLV scan. A consented subject was imaged, and the resultant image showed increased intensity in the peripheral and deeper cornea and anterior chamber. Continuous focusing with CLV spiral scanning is a promising design change to OCT systems allowing adequate focus over relatively large depths such as for scanning the human cornea.