Coherent imaging systems, such as synthetic aperture radar (SAR), often suffer from granular speckle noise due to inherent defects, which can make interpretation challenging. Although numerous despeckling methods have been proposed in the past three decades, SAR image despeckling remains a challenging task. With the extensive use of non-local self-similarity, despeckling methods under the non-local framework have become increasingly mature. However, effectively utilizing patch similarities remains a key problem in SAR image despeckling. This paper proposes a three-dimensional (3D) SAR image despeckling method based on searching for similar patches and applying the high-order singular value decomposition (HOSVD) theory to better utilize the high-dimensional information of similar patches. Specifically, the proposed method extends two-dimensional (2D) to 3D for SAR image despeckling using tensor patches. A new, non-local similar patch-searching measure criterion is used to classify the patches, and similar patches are stacked into 3D tensors. Lastly, the iterative adaptive weighted tensor cyclic approximation is used for SAR image despeckling based on the HOSVD method. Experimental results demonstrate that the proposed method not only effectively reduces speckle noise but also preserves fine details.