To solve the problem that it is hard to find the nonconvex approximation of tensor rank by using nuclear norm in infrared patch tensor model, the obtained non optimal solution further affects. For infrared small target detection, an infrared small target detection algorithm based on dehazing enhancement and tensor recovery is proposed. Firstly, the improved dark channel algorithm is used to dehaze and enhance the infrared image, which improves the definition and indirectly enhances the low rank of the background in the infrared image; Secondly, the matching tensor frontal slices are selected to construct the infrared patch tensor model. Under the framework of tensor singular value decomposition, the detection task is transformed into tensor recovery problem; Finally, a fast algorithm is designed to recover the low rank components and sparse components in the infrared image, which is simple and reduces the complexity of the algorithm. Compared with the methods of filtering and human visual system, the false detection rate of the algorithm in complex background is reduced by 16.6% on average. In common highlighted background areas, the detection performance is good, and the false detection rate can be reduced by 33%. Experimental results show that the algorithm can be applied to complex scenes and eliminate potential false alarm points.