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Although the literature has highlighted that a firm’s board is critical for firm innovation, the impact of board characteristics on firm innovation has always been examined separately, leading to inconclusive research results. Based on the complexity theory, this paper incorporates four board characteristics, including board size, board ownership, board independence and CEO duality, to examine the impact of the combinations of different board characteristics on firm innovation through qualitative comparative analysis.

Using the panel data of listed manufacturing firms in China from 2007 to 2022, this paper conducted the fuzzy set qualitative comparative analysis to test the proposed hypotheses.

The research results show that no single board characteristic can explain firm innovation, as board size, board ownership, board independence and CEO duality can lead to either positive or negative firm innovation. Moreover, firm innovation depends on a complex combination of board characteristics.

This paper makes the following contributions: Firstly, this paper advances the firm innovation literature by extending the role of board characteristics on firm innovation, thereby offering a new way to model firm innovation in terms of board characteristics. Secondly, this paper provides a more comprehensive account of the role of a firm’s board by integrating agency theory and resource dependence theory. Thirdly, this paper also identifies a promising avenue for further research in the field of corporate governance: the investigation of other contingency contexts in which the effect of board characteristics may be observed, with the aim of further increasing the understanding of board functioning.