In　intelligent　transportation　systems,　deep　learning　is　a　widely　adopted　technique　for　traffic　data　recovery.　In　city-wide　traffic　data　recovery　tasks,　traditional　centralized　deep-learning-model　training　strategies　become　inapplicable　because　of　the　expensive　storage　costs　for　large-scale　traffic　datasets.　In　this　scenario,　edge　computing　emerges　as　a　natural　choice,　allowing　decentralized　data　storage　and　distributed　training　on　edge　nodes.　However,　there　is　still　a　challenge:　distributed　training　on　edge　nodes　suffers　from　high　communication　costs　for　parameter　transmission.　In　this　paper,　we　propose　a　communication-efficient　Graph-Tensor　Fast　Iterative　Shrinkage-Thresholding　Algorithm-based　neural　Network　(GT-FISTA-Net)　for　distributed　traffic　data　recovery.　Firstly,　we　model　the　recovery　task　as　a　graph-tensor　completion　problem　to　better　capture　the　low-rankness　of　traffic　data.　A　recovery　guarantee　is　also　provided　to　characterize　the　performance　bounds　of　the　proposed　scheme　in　terms　of　recovery　error.　Secondly,　we　propose　a　distributed　graph-tensor　completion　algorithm　and　unfold　it　into　a　deep　neural　network　called　GT-FISTA-Net.　GT-FISTA-Net　requires　small　communication　costs　for　distributed　model　training　on　edge　nodes　and　thus　it　is　applicable　for　city-wide　traffic　data　recovery.　Extensive　experiments　on　real-world　datasets　show　that　the　proposed　GT-FISTA-Net　can　also　provide　excellent　recovery　accuracy　compared　with　state-of-the-art　distributed　recovery　methods.　©　2013　IEEE.