This paper proposes a method based on the deep learning (DL) networks to identify the early stage gastric cancer lesions in the narrow-band-imaging (NBI) gastroscopic images of the stomach. First, the NBI gastroscopic images with labeled lesion areas are sent to the DL network for the training purpose. Then the classifier can automatically identify and predict the lesion region in the test images. We also discuss how to improve the detection accuracy by using the data augmentation schemes when only a small number of training images are available. We use the pyramid spatial pooling (PSP) module in the U-net model to collect different levels of features, which are useful to improve the training results. In our experiments, we used 66 and 60 training and test images, respectively. The highest average precision rate and the largest average intersection-over-union (IoU) of the proposed PSP U-net model are 0.9 and 0.59, respectively.