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Bird and Davis-Nozemack (2018) theorize that tax avoidance is a sustainability problem, and offer no empirical evidence to support it. Considering that innovation is the key to solve the sustainability problem and tax avoidance is one of the sources of capital needed for innovation, this paper demonstrates that tax avoidance is a sustainability problem from the perspective of innovation. Using the data of A-share listed enterprises in China for analysis, comprehensively consider “book-tax difference” tax avoidance strategy and “book-tax conforming” tax avoidance strategy. The results show that, in general, tax avoidance has a significant negative impact on innovation input and innovation output, that is, tax avoidance inhibits innovation. Dividing the sample enterprises into technology-intensive industries, capital-intensive industries, and labor-intensive industries, the effects of tax avoidance on innovation remains robust. We further examine the impact of external monitors and FinTech on the relationship between tax avoidance and innovation, and the results show that they both reinforce the negative impact of tax avoidance on innovation. This study is of great significance for tax policy-making in support of innovation.