Gastric precancerous diseases (GPD) may deteriorate into early gastric cancer if misdiagnosed, so it is important to help doctors recognize GPD accurately and quickly. In this paper, we realize the classification of 3-class GPD, namely, polyp, erosion, and ulcer using convolutional neural networks (CNN) with a concise model called the Gastric Precancerous Disease Network (GPDNet). GPDNet introduces fire modules from SqueezeNet to reduce the model size and parameters about 10 times while improving speed for quick classification. To maintain classification accuracy with fewer parameters, we propose an innovative method called iterative reinforced learning (IRL). After training GPDNet from scratch, we apply IRL to fine-tune the parameters whose values are close to 0, and then we take the modified model as a pretrained model for the next training. The result shows that IRL can improve the accuracy about 9% after 6 iterations. The final classification accuracy of our GPDNet was 88.90%, which is promising for clinical GPD recognition.