Optical coherence tomography (OCT) is a high-resolution and non-invasive optical imaging technology, which is widely used in many fields. Nevertheless, OCT images are disturbed by speckle noise due to the low-coherent interference properties of light, resulting in significant degradation of OCT image quality. Therefore, a denoising algorithm of OCT images via sparse representation based on noise estimation and global dictionary is proposed in this paper. To remove noise and improve image quality, the algorithm first constructs a global dictionary from high-quality OCT images as training samples and then estimates the noise intensity for each input image. Finally, the OCT images are sparsely decomposed and reconstructed according to the global dictionary and noise intensity. Experimental results indicate that the proposed algorithm efficiently removes speckle noise from OCT images and yield high-quality images. The denoising effect and execution efficiency are evaluated based on quantitative metrics and running time, respectively. Compared with the mainstream adaptive dictionary denoising algorithm in sparse representation and other denoising algorithms, the proposed algorithm exhibits satisfying results in terms of speckle-noise reduction as well as edge preservation, at a reduced computational cost. Moreover, the final denoising effect is significantly better for sets of images with significant variations in noise intensity.