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Transformer based on self-attention mechanism is blooming in computer vision nowadays. However, its application to video quality assessment (VQA) has not been reported. Evaluating the quality of in-the-wild videos is challenging due to the unknown of pristine reference and shooting distortion. This paper presents a novel space-time attention network for the VQA problem, named StarVQA. StarVQA builds a Transformer by alternately concatenating the divided space-time attention. To adapt the Transformer architecture for training, StarVQA designs a vectorized regression loss by encoding the mean opinion score (MOS) to the probability vector and embedding a special vectorized label token as the learnable variable. To capture the long-range spatiotemporal dependencies of a video sequence, StarVQA encodes the space-time position information of each patch to the input of the Transformer. Various experiments are conducted on the de-facto in-the-wild video datasets, including LIVE-VQC, KoNViD-1k, LSVQ, and LSVQ-1080p. Experimental results demonstrate the superiority of StarVQA over the state-of-the-art. The source code is available at https://github.com/GZHU-DVL/StarVQA.