Multivariate Time Series (MTS) forecasting is an essential problem in many fields. Accurate forecasting results can effectively help in making decisions. To date, many MTS forecasting methods have been proposed and widely applied. However, these methods assume that the predicted value of a single variable is affected by all other variables, ignoring the causal relationship among variables. To address the above issue, we propose a novel end-to-end deep learning model, termed graph neural network with neural Granger causality, namely CauGNN, in this paper. To characterize the causal information among variables, we introduce the neural Granger causality graph in our model. Each variable is regarded as a graph node, and each edge represents the casual relationship between variables. In addition, convolutional neural network filters with different perception scales are used for time series feature extraction, to generate the feature of each node. Finally, the graph neural network is adopted to tackle the forecasting problem of the graph structure generated by the MTS. Three benchmark datasets from the real world are used to evaluate the proposed CauGNN, and comprehensive experiments show that the proposed method achieves state-of-the-art results in the MTS forecasting task.