Aiming at the problems of difficult detection of infrared small targets in cloud background and few available data sets, a detection method based on chaotic prediction is proposed. Based on the spatial chaotic characteristics of cloud background, the prediction model of chaotic sequence is designed by using radial basis function neural network, and the network parameters are optimized by genetic algorithm to improve the prediction accuracy. Finally, the small target detection is realized by the prediction error of the image pixel sequence by the prediction model. Experiments verify the effectiveness of the above algorithm. The detection rate of test samples is 86.7% and the false alarm rate is 0.86%.