With the application of lightning data in meteorology, electric power as well as public safety, massive lightning data is accumulated. Meanwhile, a synthesized and complicated problem arose, which is, how to automatically obtain the valuable information from the massive lightning data. The deep learning method provides an effective way to automatically classify the event type of lightning discharges from raw lightning data. In this paper, we propose a five-category classification model for the raw lightning waveforms in VLF/LF bands. The model is based on deep convolutional neural network, which is trained and tested by a six year (2012-2017) data set that comprised of over 30000 lightning events. We did experiment with different layers of networks and found that the 7-layer network gives the best performance. The output of the classifier is a five-element vector which shows up the results of different lightning type. Due to the multi-layer stacking of the convolutional network, higher-order features can be better extracted. Furthermore, the model we proposed can effectively identify the cloud-to-ground (CG) flash, ordinary intracloud (IC) flash, preliminary breakdown pulse (PB), narrow bipolar event (NBE), and especially the error rate on CG is less than 3%. Finally, we apply the classifier to the lightning data set for 2017 and group identified return stroke into flashes by hand to qualify the accuracy-stroke-study data of CG flashes. Based on the flashes, we present the characteristics of cloud-to-ground lightning flashes in four isolated small thunderstorms.