Semiconductor quantum dots (QDs) are extremely interesting materials for the development of photovoltaic devices, but currently the present the drawback is that the most efficient devices have been prepared with toxic heavy metals of Cd or Pb. Solar cells based on "green" QDs--totally free of Cd or Pb--present a modest efficiency of 2.52%. Herein we achieve effective surface passivation of the ternary CuInS2 (CIS) QDs that provides high photovoltaic quality core/shell CIS/ZnS (CIS-Z) QDs, leading to the development of high-efficiency green QD solar cells that surpass the performance of those based on the toxic cadmium and lead chalcogenides QDs. Using wide absorption range QDs, CIS-Z-based quantum dot sensitized solar cell (QDSC) configuration with high QD loading and with the benefit of the recombination reduction with type-I core/shell structure, we boost the power conversion efficiency of Cd- and Pb-free QDSC to a record of 7.04% (with certified efficiency of 6.66%) under AM 1.5G one sun irradiation. This efficiency is the best performance to date for QDSCs and also demonstrates that it is possible to obtain comparable or even better photovoltaic performance from green CIS QDs to the toxic cadmium and lead chalcogenides QDs.