Smart technology brings convenience to our lives, and smart medical diagnosis plays a particularly important role in smart cities and the smart world. In smart diagnosis, high-quality image labels are essential for supervised medical image learning. The correctness of labels has a substantial influence on smart disease diagnosis. However, the labelling of disease images by professional doctors is a time-consuming and labour-intensive project; therefore, obtaining correct and high-quality labels is a difficult task. This paper proposes a deep convolutional neural network (CNN)-based label completion and correction method (LCC) for supervised medical image learning in smart diagnosis. We use a small number of labelled images in a dataset to train a model, and design a strategy to complement most of the unlabelled data and correct noise label data, and then use the results of completion and correction to continually modify the model to achieve better results. We take the diagnosis of Seborrheic Keratosis (SK) and Flat Wart (FW) as examples; the experimental results show that this strategy can use limited labelled data to complete the labels for most of the unlabelled data and correct some noise labels in the dataset, which improves the accuracy rate of the model to identify diseases.