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• Accelerating the adoption of green innovation is beneficial for an urban economy. • Command-and-control environmental regulations neither stimulate nor inhibit green innovation in Xi'an. • Market-based and voluntary environmental regulations effectively stimulate urban green innovation. • There is an inverted U relationship between environmental regulation and green innovation efficiency. While balancing economic progress and environmental pollution, environmental regulation plays a vital role conditioning green innovation. However, most research focuses on the effect of such regulations at the industry- or regional-level, lacking city-level analysis. Using the city of Xi'an (China) as a case study, environmental regulations and their effect on urban green innovation are analysed. First, using a slacks-based measure of directional distance functions (SBM-DDF) model we measure the green innovation efficiency of Xi'an from 2003 to 2016. Regression analysis is then used to explore the green innovation effect under the implementation of three environmental regulations, including command-and-control, market-based, and voluntary. Results indicate that market-based and voluntary regulations are more efficient at stimulating green innovation than command-and-control environmental regulations. The environmental regulations and green innovation efficiency also have non-linear inverted U-shape relationships. The findings will help policy makers to design more effective environmental regulations. [ABSTRACT FROM AUTHOR]