Swept-source optical coherence tomography (SS OCT) is a noninvasive, cross-sectional imaging modality that has been widely used in diagnostic medicine. Currently, SS OCT still suffers from motion artifacts and noise. In this paper, we present a novel technique, based on the compressive sensing (CS) principle, for fast super-resolution reconstruction of SS OCT. We utilize a lower spatial sampling rate to reduce the total acquisition time. SS OCT images are reconstructed by solving an optimization problem that minimizes the \({L}_{1/2}\) norm of a transformed image to enforce sparsity, subject to data consistency constraints. We tested our algorithms on uniformly undersampled spectral data. Experiments showed that our algorithm could reconstruct high-resolution SS OCT images while reducing the total acquisition and imaging time.