Firm's effort on Green technology innovation (hereafter, called G-innovation) is affected by financing constraints, and firm will make a discretionary choice according to its own situation, to achieve the maximization of self-interests. Based on the data of Chinese micro enterprises, firstly, we empirically analyze firms' decision-making towards G-innovation when faced with financing constraints. It supports the view that financing constraints can hinder enterprise technological innovation. And we also make an explanation that the social benefits of green technology innovation are greater than personal benefits, which makes enterprises tend to reduce green technology innovation when facing financing constraints. Then we examine firms' heterogonous behaviors under different internal attributes and external environments. The results reveal that: First, firms are reluctant to pay more efforts to G-innovation when faced with increased financing constraints. Second, firms with different attributes exhibit heterogeneous G-innovation. Political connections will change firms' willingness to innovate, while the structure of property rights and the pollution degree will not. Third, firms under different external environment also exhibit heterogeneous G-innovation. When economic policy uncertainty increases, firms' willingness to innovate weakens. The development of shadow banks fail to improve firm's willingness to innovate.