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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.