Full-field swept-source optical coherence tomography (FF-SS-OCT) was recently shown to allow new and exciting applications for imaging the human eye that were previously not possible using current scanning OCT systems. However, especially when using cameras that do not acquire data with hundreds of kHz frame rate, uncorrected phase errors due to axial motion of the eye lead to a drastic loss in image quality of the reconstructed volumes. Here we first give a short overview of recent advances in techniques and applications of parallelized OCT and finally present an iterative and statistical algorithm that estimates and corrects motion-induced phase errors in the FF-SS-OCT data. The presented algorithm is in many aspects adopted from the phase gradient autofocus (PGA) method, which is frequently used in synthetic aperture radar (SAR). Following this approach, the available phase errors can be estimated based on the image information that remains in the data, and no parametrization with few degrees of freedom is required. Consequently, the algorithm is capable of compensating even strong motion artifacts. Efficacy of the algorithm was tested on simulated data with motion containing varying frequency components. We show that even in strongly blurred data, the actual image information remains intact, and the algorithm can identify the phase error and correct it. Furthermore, we use the algorithm to compensate real phase error in FF-SS-OCT imaging of the human retina. Acquisition rates can be reduced by a factor of three (from 60 to 20 kHz frame rate) with an image quality that is even higher compared to uncorrected volumes recorded at the maximum acquisition rate. The presented algorithm for axial motion correction decreases the high requirements on the camera frame rate and thus brings FF-SS-OCT closer to clinical applications.