ABSTRACT Using 2009 to 2020 data for Chinese A-share listed firms in Shanghai and Shenzhen, we examine how much state ownership in firms is most conducive to improving corporate innovation quantity and quality. Our results are as follows: First, state ownership enhances corporate innovation by alleviating financing constraints (resource availability) but inhibits corporate innovation by weakening risk-taking (innovation willingness) and increasing agency costs (resource efficiency), leading to an inverted U-shaped relationship between state ownership and corporate innovation. Second, the percentage of state ownership that maximises innovation quality differs from that of maximising innovation quantity. State-owned enterprises (SOEs) can choose an appropriate state-ownership structure according to the actual situation in the mixed-ownership reform process. Third, non-state-owned shareholders’ control right negatively moderates the inverted U-shaped relationship between state ownership and innovation quantity but do not significantly moderate the inverted U-shaped relationship between state ownership and innovation quality. Fourth, foreign direct investment (FDI) negatively moderates the inverted U-shaped relationship between state ownership and innovation quantity and quality. Our findings reveal the impact of state ownership on corporate innovation and its transmission path, providing empirical evidence for optimising the ownership structure based on a corporate innovation perspective in the process of SOE mixed-ownership reform.