Aiming at the problems of difficult detection of infrared small targets in cloudy background with few available data sets, a detection method based on chaos prediction was proposed. Based on the spatial chaotic characteristics of cloudy background, the prediction model of chaotic sequence was designed by using radial basis function neural network, and the network parameters were optimized by genetic algorithm to improve the prediction accuracy. Then, the small target detection was realized by the prediction error between the predicted and actual values 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%.