In order to reduce the computational complexity of the infrared small targets detection algorithm based on tensor low-rank sparse decomposition and improve the detection performance of infrared dim targets, an infrared small target detection algorithm based on the randomized tensor algorithm was proposed. The algorithm combines the spatial-temporal tensor of the image with the randomized algorithm. Firstly, the infrared image sequence was constructed into spatial-temporal tensors as the input of the tensor optimization model, and then the randomized tensor algorithm was applied to solve the tensor optimization problem. Finally, the target image was obtained by restoring the calculated sparse tensor to the image. The results demonstrate that compared with the traditional algorithm based on low-rank sparse decomposition, the proposed algorithm is faster and also has good detection performance. This study provides a reference for the algorithm acceleration of infrared small target detection based on tensor low-rank sparse decomposition.