Green innovation investments have rapidly grown since 2000. Green innovation indexes play important roles and are typically constructed by screening and indexing. However, Nobel Laureate Markowitz emphasizes portfolio selection instead of security selection and accentuates that “A good portfolio is more than a long list of good stocks.” Moreover, the screening-indexing strategies ignore that investors can take green innovation as an additional objective and thus gain additional utility. We consequently construct 3-objective portfolio selection for green innovation in addition to variance (...) and expected return. An efficient frontier of portfolio selection then extends to an efficient surface which is a panorama of the optimal variance, expected return, and expected green innovation. Investors thus fully envisage the trade-offs and enjoy the freedom of choosing preferred portfolios on the surface. In contrast, the screening-indexing strategies inflexibly leave investors with only one point. As the originality, we prove in a theorem that there typically exists a curve on the efficient surface so all portfolios on the curve dominate the green innovation index. We test the dominance by component stocks of China Securities Index 300 and obtain affirmative results out of sample. The results still hold in robustness tests. At last, we classify green innovation into categories, further model the categories by general k -objective portfolio selection, and still illustrate the dominance. Consequently, investors can consider and control each category. (shrink)