Green innovation makes economic growth rely on scientific and technological innovation, replaces the traditional cheap labor and energy-driven economic development mode, achieves the goal of ecological environment improvement and sustainable development, and realizes the green development of the society as a whole. In this paper, China’s catering industry is selected as a specific research object, a system of indicators for measuring green innovation efficiency is built, an SBM-DEA model based on non-expected outputs is constructed, and the Malmquist-Luenberger productivity index is introduced to improve the model, realizing the evaluation of the green innovation efficiency of the catering industry in 30 provinces and regions of China. Meanwhile, the convergence status of regional and national green innovation efficiency development is explored according to the development status of green innovation efficiency in China as a whole and in the East and West. The efficiency values of green innovation in the two stages of technology development and industrialization are 0.6149 and 0.8751, respectively. The efficiency value of the second stage is significantly higher than that of the first stage. Meanwhile, through regional comparison, it can be seen that the green technology innovation efficiency has a clear gap between regions, and the dynamic efficiency value of green technology innovation in most of China’s provincial administrative units is greater than 1. In addition, from 2014 to 2023, the change trend presented by the inter-regional differences in the green innovation efficiency of China’s food and beverage industry in the East-Central, East-West, and Center-West is in the overall decreasing trend, that is, the food and beverage industry green innovation efficiency has convergence, which provides data support for the development of relevant decisions.