Corneal evaluation in ophthalmology necessitates cellular-resolution and fast imaging techniques allowing accurate diagnoses. Currently, the fastest volumetric imaging technique is Fourier-domain full-field optical coherence tomography (FD-FF-OCT) that uses a fast camera and a rapidly tunable laser source. Here, we demonstrate high-resolution, highspeed, non-contact corneal volumetric imaging in vivo with FD-FF-OCT that can acquire a single 3D volume with a voxel rate of 7.8 GHz. The spatial coherence of the laser source was suppressed to prevent it from focusing to a spot on the retina, and therefore, exceeding the maximum permissible exposure (MPE). Inherently volumetric nature of FD-FF-OCT data enabled flattening of curved corneal layers. Acquired FD-FF-OCT images revealed corneal cellular structures, such as epithelium, stroma and endothelium, as well as subbasal and midstromal nerves.