The application of green technologies can reduce environmental hazards and promote sustainability. The connotation of green technology innovation has two main aspects: the first aspect is the generation of green technology from nothing to something, and the other aspect is the improvement and upgrading of existing green technology; these two aspects are related. However, from the existing research, there are relatively few studies on the process of green technology innovation from these two aspects at the same time. If green technology is not studied from this perspective, the evolutionary process and influencing factors of green technology from generation to development cannot be clarified, which is not conducive to the development of green technology and the realization of the goal of environmental friendliness. Research considers the green innovation process from R&D to upgrading linkages and analyses the roles of government departments, green technology R&D institutions, and green technology application enterprises in green technology innovation. In addition, the green technology application enterprises are considered to promote technology enhancement through technology application feedback with green technology R&D institutions. The evolutionary game model of three subjects was established, the strategic evolution process of different subjects was analyzed, the influence of each element on the strategic choice of different subjects was explored, and the stability analysis of strategic choice was conducted using simulation software. The study shows the following: (1) The greater the government’s punishment and support to green technology R&D institutions, the more favorable it is for green technology R&D institutions to carry out green technology R&D. (2) In green technology applications, if the government has no direct interest relationship with green technology application enterprises, the enterprises will choose negative response behavior. (3) The greater the technology enhancement gains of green technology R&D institutions and the greater the feedback gains of technology applications actively carried out by enterprises in response to the government’s call, the more the government departments tend to support green technology R&D.