Abstract: Sunspots are closely linked with flares eruption.Detecting the sunspots from full-disk continuous images timely and accurately could provide clues to predict flares. In this paper, we implement a new detecting method for sunspots from HMI full-disk continuous images, which is based on convolutional neural network LeNet-5 under the deep-learning framework. A sample library of sunspots is set up, and a full convolutional neural network named as Sunspotsnet is trained, and finally a detection method for sunspots from full-disk continuous images based on Sunspotsnet is proposed. The results show that this method can detect the different kinds of sunspots, especially faint pores (0.88 < I__QS>). It is feasible to detect the sunspots from full-disk continuous images based on deep-learning technology. This trained convolutional neural network Sunspotsnet can be deployed in detecting the sunspots quickly and effectively.