According to the World Health Organization (WHO), corneal diseases alongside with cataract and retinal diseases are major causes of blindness worldwide. For the 95.5% of corneal blindness cases, prevention or rehabilitation could have been possible without negative consequences for vision, provided that disease is diagnosed early. However, diagnostics at the early stage requires cellular-level resolution, which is not achieved with routinely used Slit-lamp and OCT instruments. Confocal microscopy allows examination of the cornea at a resolution approaching histological detail, however requires contact with a patient’s eye. The recently developed full-field OCT technique, in which 2D en face tangential optical slices are directly recorded on a camera, was successfully applied for ex vivo eye imaging. However, in vivo human eye imaging has not been demonstrated yet. Here we present a novel non-contact full-field OCT system, which is capable of imaging in air and, therefore, shows potential for in vivo cornea imaging in patients. The first cellular-level resolution ex vivo images of cornea, obtained in a completely non-contact way, were demonstrated. We were able to scan through the entire cornea (400 µm) and resolve epithelium, Bowman’s layer, stroma and endothelium. FFOCT images of the human cornea in vivo were obtained for the first time. The epithelium structures and stromal keratocyte cells were distinguishable. Both ex vivo and in vivo images were acquired with a large (1.26 mm x 1.26 mm) field of view. Cellular details in obtained images make this device a promising candidate for realization of high-resolution in vivo cornea imaging.