To investigate the relationships between financial constraints, government subsidies, and corporate innovation, a semi-logarithmic fixed-effect panel model and mediation effect test were applied, based on the data of Chinese listed companies from 2007 to 2017. We find that (1) financial constraints suppress corporate innovation. (2) Government subsidies are targeted at bailing out firms facing financial constraints. (3) Government subsidies promote corporate innovation (4) Government subsidies partially offset the suppression of financial constraints on innovation. We contribute to the fields of public finance, corporate finance, and corporate innovation by: (1) justifying the government subsidies target strategy as a bailout of corporate financial constraints, (2) verifying the corporate-innovation promotion of government subsidies, thus justifying the efficiency of government subsidies, and (3) showing that different types of innovation benefit differently from subsidies, thus justifying subsidies as a structural innovation engine.