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In order to expand the prediction range of spatio-temporal graph convolutional networks and apply them to the multivariate time series prediction problems in the scenario of unknown correlation, this paper proposed a graph learning based spatio-temporal graph convolutional networks（GLB-STGCN）. The graph learning layer learned the graph adjacency matrix from the time series with the help of cosine similarity, then the graph convolution networks captured the interaction between multi-variables, and finally the multi-kernel time convolution networks captured the periodic characteristics of the time series for precise prediction. To verify the effectiveness of GLB-STGCN, this paper used 4 public datasets from astronomy, electricity, transportation and economy and 1 industrial production dataset for the prediction experiments. The results showed that GLB-STGCN outperforms the comparison methods, especially on astronomical datasets, with prediction errors reduced by 6.02%, 8.01%, 6.72%, and 5.31%, respectively. The experimental results proved that GLB-STGCN has a wider application range and better prediction effect, especially for time series prediction problems with obvious natural cycles. [ABSTRACT FROM AUTHOR]