Accurate　traffic　forecasting　is　important　to　enable　intelligent　transportation　systems　in　a　smart　city.　This　problem　is　challenging　due　to　the　complicated　spatial,　short-term　temporal　and　long-term　periodical　dependencies.　Existing　approaches　have　considered　these　factors　in　modeling.　Most　solutions　apply　CNN,　or　its　extension　Graph　Convolution　Networks　(GCN)　to　model　the　spatial　correlation.　However,　the　convolution　operator　may　not　adequately　model　the　non-Euclidean　pair-wise　correlations.　In　this　paper,　we　propose　a　novel　Attention-based　Periodic-Temporal　neural　Network　(APTN),　an　end-to-end　solution　for　traffic　foresting　that　captures　spatial,　short-term,　and　long-term　periodical　dependencies.　APTN　first　uses　an　encoder　attention　mechanism　to　model　both　the　spatial　and　periodical　dependencies.　Our　model　can　capture　these　dependencies　more　easily　because　every　node　attends　to　all　other　nodes　in　the　network,　which　brings　regularization　effect　to　the　model　and　avoids　overfitting　between　nodes.　Then,　a　temporal　attention　is　applied　to　select　relevant　encoder　hidden　states　across　all　time　steps.　We　evaluate　our　proposed　model　using　real　world　traffic　datasets　and　observe　consistent　improvements　over　state-of-the-art　baselines.