Aiming at the problem that infrared images face low contrast between the background and the target and insufficient noise suppression ability under the complex cloud background, an infrared small target detection method based on the tensor nuclear norm and direction residual weighting is proposed. Based on converting the infrared image into a tensor model, from the perspective of the low-rank nature of the background tensor, and taking advantage of the difference in contrast between the background and the target in different directions, we design a double-neighborhood local contrast based on direction residual weighting method (DNLCDRW) combined with the partial sum of tensor nuclear norm (PSTNN) to achieve effective background suppression and recovery of infrared small targets. Experiments show that the algorithm is effective in suppressing the background and improving the detection ability of the target.