Optical coherence tomography (OCT) is an important interferometric diagnostic technique, which provides cross-sectional views of biological tissues’ subsurface microstructures. However, the imaging quality of high-speed OCT is limited by the large speckle noise. To address this problem, we propose a multiframe 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 the constraints from logarithmic image formation and nonuniform noise variance. In addition, 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.