Learning　brain　effective　connectivity　networks　(ECN)　from　functional　magnetic　resonance　imaging　(fMRI)　data　has　gained　much　attention　in　recent　years.　With　the　successful　applications　of　deep　learning　in　numerous　fields,　several　brain　ECN　learning　methods　based　on　deep　learning　have　been　reported　in　the　literature.　However,　current　methods　ignore　the　deep　temporal　features　of　fMRI　data　and　fail　to　fully　employ　the　spatial　topological　relationship　between　brain　regions.　In　this　article,　we　propose　a　novel　method　for　learning　brain　ECN　based　on　spatiotemporal　graph　convolutional　models　(STGCM),　named　STGCMEC,　in　which　we　first　adopt　the　temporal　convolutional　network　to　extract　the　deep　temporal　features　of　fMRI　data　and　utilize　the　graph　convolutional　network　to　update　the　spatial　features　of　each　brain　region　by　aggregating　information　from　neighborhoods,　which　makes　the　features　of　brain　regions　more　discriminative.　Then,　based　on　such　features　of　brain　regions,　we　design　a　joint　loss　function　to　guide　STGCMEC　to　learn　the　brain　ECN,　which　includes　a　task　prediction　loss　and　a　graph　regularization　loss.　The　experimental　results　on　a　simulated　dataset　and　a　real　Alzheimer＇s　disease　neuroimaging　initiative　(ADNI)　dataset　show　that　the　proposed　STGCMEC　is　able　to　better　learn　brain　ECN　compared　with　some　state-of-the-art　methods.