In the aviation industry, foreign object debris (FOD) on airport runways is a serious threat to aircraft during takeoff and landing. Therefore, FOD detection is important for improving the safety of aircraft flight. In this paper, an unsupervised anomaly detection method called Multi-Scale Feature Inpainting (MSFI) is proposed to perform FOD detection in images, in which FOD is defined as an anomaly. This method adopts a pre-trained deep convolutional neural network (CNN) to generate multi-scale features for the input images. Based on the multi-scale features, a deep feature inpainting module is designed and trained to learn how to reconstruct the missing region masked by the multi-scale grid masks. During the inference stage, an anomaly map for the test image is obtained by computing the difference between the original feature and its reconstruction. Based on the anomaly map, the abnormal regions are identified and located. The performance of the proposed method is demonstrated on a newly collected FOD dataset and the public benchmark dataset MVTec AD. The results show that the proposed method is superior to other methods.