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Trajectory prediction is one of the core functions of autonomous driving. Modeling spatial-aware interactions and temporal motion patterns for observed vehicles are critical for accurate trajectory prediction. Most recent works on trajectory prediction utilize recurrent neural networks (RNNs) to model temporal patterns and usually need convolutional neural networks (CNNs) additionally to capture spatial interactions. Although Transformer, a multi-head attention-based network, has shown its notable ability in many sequence-modeling tasks (e.g., machine translation in natural language processing), it has not been explored much in trajectory prediction. This paper presents a Spatial Interaction-aware Transformer-based model, which uses the multi-head self-attention mechanism to capture both interactions of neighbor vehicles and temporal dependencies of trajectories. This model applies a GRU-based encoder-decoder module to make the prediction. Besides, different from methods considering the spatial interactions only among observed trajectories in both encoding and decoding stages, our model will also consider the potential spatial interactions between future trajectories in decoding. The proposed model was evaluated on the NGSIM dataset. Compared with other baselines, our model exhibited better prediction precision, especially for long-term prediction. [ABSTRACT FROM AUTHOR]