Innovation is the first driving force for development, and it is the "bull's nose" that affects the overall economic and social development. Regional innovation efficiency measures a region's comprehensive innovation performance with the input-output ratio of innovation, and its influencing factors exist in many aspects. Financial deepening is an important indicator to measure the level of financial development. In order to study the interaction between financial deepening and regional innovation efficiency in various countries and its internal mechanism, the authors first use DEA method of multi-input and multi-output to measure the regional innovation efficiency of 80 countries, and then use Tobit model to make an empirical analysis of 80 transnational panel data from 2011 to 2018. It is found that there is a significant U-shaped curve relationship between financial deepening and regional innovation efficiency, that is, with the promotion of financial deepening, its influence on regional innovation efficiency will change from "inhibition" effect to "promotion" effect. This is because when the financial deepening is low, the development of venture loans and credit loans lags behind, the venture capital channels are imperfect, and the financial structure and market are imperfect, which leads to the backward financing and securities lending functions of multi-level and three-dimensional enterprises, thus inhibiting the innovation efficiency of enterprises. When the financial deepening is high, the venture capital channel is gradually improved, the financing cost of enterprises is low, and the financial market and financial structure are perfect, thus promoting the innovation efficiency of enterprises. The authors also find that different economic levels of different countries will also lead to significant differences in financial deepening and regional innovation efficiency. In this paper, countries are divided into developed groups and underdeveloped groups according to their economic development levels. Grouping research shows that financial deepening has a selective effect on regional innovation efficiency, that is, financial deepening has a U-shaped curve characteristic on innovation efficiency of underdeveloped countries, but there is no such effect in developed groups. The reasons are: in developed countries, the level of economic development is high, the financial structure and market are perfect, the channels of venture capital are unimpeded, and the influence of financial deepening on regional efficiency is no longer "restrained". In underdeveloped countries, however, the level of economic development is low, and the level of financial structure and financial market development is in the stage of development and perfection. For the perfect financial market and financial structure, the influence of financial deepening on regional innovation efficiency is "promoting" effect, while for the imperfect part, the influence of financial deepening on regional innovation efficiency is "inhibiting" effect. In order to test the robustness of the research results of this paper, the authors use two test methods: lag term test and substitution variable test. The test results are robust, that is, with the promotion of financial deepening, its influence on regional innovation efficiency will change from "inhibition" effect to "promotion" effect. Therefore, government departments should correctly understand the role of financial deepening in regional innovation efficiency, improve the innovation system, strengthen financial supervision, prevent and resolve financial risks, give consideration to both long-term and short-term interests, give full play to the role of financial deepening in promoting regional innovation and economic growth, and promote the financial system to better meet the innovation needs of the new era, so as to promote the improvement of regional innovation efficiency. The research of this paper has enlightenment and reference significance for developing countries that make use of financial deepening to improve innovation efficiency.