Ultrasound is a low-cost, non-invasive and real-time imaging modality that has proved popular for many medical applications. Unfortunately, the acquired ultrasound images are often corrupted by speckle noise from scatterers smaller than ultrasound beam wavelength. The signal-dependent speckle noise makes visual observation difficult. In this paper, we propose a patch-based low-rank approach for reducing the speckle noise in ultrasound images. After constructing the patch group of the ultrasound images by the block-matching scheme, we establish a variational model using the weighted nuclear norm as a regularizer for the patch group. The alternating direction method of multipliers (ADMM) is applied for solving the established nonconvex model. We return all the approximate patches to their original locations and get the final restored ultrasound images. Experimental results are given to demonstrate that the proposed method outperforms some existing state-of-the-art methods in terms of visual quality and quantitative measures.