In order to improve the management efficiency of software vulnerability classification, reduce the risk of system being attacked and destroyed, and save the cost for vulnerability repair, this paper proposes an automatic algorithm for Software Vulnerability Classification based on convolutional neural network (CNN) and gate recurrent unit neural network (GRU), called SVC-CG. It has conducted a fusion between the models of CNN and GRU according to their advantages (CNN is good at extracting local vector features of vulnerability text and GRU is good at extracting global features related to the context of vulnerability text). The merger of the features extracted by the complementary models can represent the semantic and grammatical information more accurately. Firstly, the Skip-gram language model based on Word2Vec is used to train and generate the word vector, and the words in each vulnerability text are mapped into the space with limited dimensions to represent the semantic information. Then the CNN is used to extract the local features of the text vector, and the GRU is used to extract the global features related to the text context. We combine two complementary models to construct a SVC-CG neural network algorithm, which can represent semantic and grammatical information more accurately to realize automatic classification of vulnerabilities. The experiment uses the vulnerability data from the national vulnerability database (NVD) to train and evaluate the SVC-CG algorithm. Through experimental comparison and analysis, the SVC-CG algorithm proposed in this paper has a good performance on Macro recall rate, Macro precision rate and Macro F1-score.