A new procedure for detecting weak and small infrared targets in the background clutter was presented. Based on the spatial correlation property of the infrared radiation of the background, the spatial distribution of the infrared radiation of the background clutter was predicted by the approach of LMS adaptive spatial predicting filtering, and the moving infrared targets were detected by the predicting error. The method to improve the predicted quality was also discussed. Finally, some experimental results for practical infrared images were presented to show the effect of the procedure.