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Arbitrary neural style transfer is a vital topic with great research value and wide industrial application, which strives to render the structure of one image using the style of another. Recent researches have devoted great efforts on the task of arbitrary style transfer (AST) for improving the stylization quality. However, there are very few explorations about the quality evaluation of AST images, even it can potentially guide the design of different algorithms. In this paper, we first construct a new AST images quality assessment database (AST-IQAD), which consists 150 content-style image pairs and the corresponding 1200 stylized images produced by eight typical AST algorithms. Then, a subjective study is conducted on our AST-IQAD database, which obtains the subjective rating scores of all stylized images on the three subjective evaluations, i.e., content preservation (CP), style resemblance (SR), and overall vision (OV). To quantitatively measure the quality of AST image, we propose a new sparse representation-based method, which computes the quality according to the sparse feature similarity. Experimental results on our AST-IQAD have demonstrated the superiority of the proposed method. The dataset and source code will be released at https://github.com/Hangwei-Chen/AST-IQAD-SRQE