Optical coherence tomography (OCT) is an important interferometric diagnostic technique which provides cross-sectional views of the subsurface microstructure of biological tissues. However, the imaging quality of high-speed OCT is limited due to the large speckle noise. To address this problem, this paper proposes a multi-frame algorithmic method to denoise OCT volume. Mathematically, we build an optimization model which forces the temporally registered frames to be low rank, and the gradient in each frame to be sparse, under logarithmic image formation and noise variance constraints. Besides, a convex optimization algorithm based on the augmented Lagrangian method is derived to solve the above model. The results reveal that our approach outperforms the other methods in terms of both speckle noise suppression and crucial detail preservation.