Acute myeloid leukemia (AML) is an aggressive and lethal blood cancer originating from rare populations of leukemia stem cells (LSCs). AML relapse after conventional chemotherapy is caused by a remaining population of drug-resistant LSCs. Selective targeting of the chemoresistant population is a promising strategy for preventing and treating AML relapse. Polycomb repressive complex 2 (PRC2) trimethylates histone H3 at lysine 27 to maintain the stemness of LSCs. Here, we show that quiescent LSCs expressed the highest levels of enhancer of zeste (EZH) 1 and EZH2, the PRC2 catalytic subunits, in the AML hierarchy, and that dual inactivation of EZH1/2 eradicated quiescent LSCs to cure AML. Genetic deletion of Ezh1/2 in a mouse AML model induced cell cycle progression of quiescent LSCs and differentiation to LSCs, eventually eradicating AML LSCs. Quiescent LSCs showed PRC2-mediated suppression of Cyclin D, and Cyclin D-overexpressing AML was more sensitive to chemotherapy. We have developed a novel EZH1/2 dual inhibitor with potent inhibitory activity against both EZH1/2. In AML mouse models and patient-derived xenograft models, the inhibitor reduced the number of LSCs, impaired leukemia progression, and prolonged survival. Taken together, these results show that dual inhibition of EZH1/2 is an effective strategy for eliminating AML LSCs.