Considering the false alarm and real-time requirements of infrared small-target detection under a complex cloud background, a novel algorithm is proposed based on structure tensor screening and local contrast analysis. Combined with the feature that the maximum eigenvalue of the structure tensor of the target area is larger than that of other background areas, the proposed algorithm can filter out most nontarget areas and retain a few suspicious areas. Local contrast calculation performed on suspicious areas can enhance the target, suppress the residual background, and effectively reduce computation. The algorithm steps are as follows: first, we constructed the structure tensor matrix within the local image area captured by the sliding window, and where the maximum eigenvalue is larger than the threshold is marked as a suspicious area. Then, we calculated the ratio-difference joint local contrast. Finally, we adopted an adaptive threshold segmentation on the saliency map to extract the real target. Experimental results showed that the proposed algorithm can achieve a higher detection rate, lower false alarm rate, and shorter running time under a complex cloud background.