Multi-focus image fusion is the process of fusing images of the same scene with different focus ranges. However, pixel misclassification and artifacts caused by noise have been unavoidable problems in fusion methods. To overcome this problem, we propose gradient tensor high-order singular value decomposition (HOSVD) to fuse multi-focus images. The eight-direction Sobel gradient operator is used to obtain second-order gradients in different directions. Tensor-based information processing can effectively represent high-dimensional information and extract structural information from multi-focus images. Therefore, second-order gradient matrices of different images are formed into tensors. The gradient tensor of the images is transformed by HOSVD to obtain the core tensor and factor matrixes. The images are better represented by multiplying the core tensor with the factor matrix corresponding to the direction of the image. In the core tensor, the larger singular values represent basic information and the small singular values high-frequency information. The noise generally belongs to high-frequency information, so we select the larger singular values in the core tensor as activity level variables of the image to reduce noise. Experimental results demonstrate that the proposed fusion method can effectively reduce noise effects and achieve state-of-the-art fusion performance in both objective metrics and visual quality.