Ammonia has recently received much attention as a novel clean energy with broad application prospects. The paper focuses on the extinction limits of dimethyl ether/ammonia mixtures cool and hot diffusion flames by an atmospheric counterflow burner. The low and high temperature chemical kinetics of dimethyl ether/ammonia are analyzed. The results show that the extinction limits of dimethyl ether/ammonia mixtures cool and hot diffusion flames decrease with the increase of the ammonia blend ratios. For dimethyl ether/ammonia cool flames, the low temperature reactivity of dimethyl ether is inhibited mainly through three aspects: ammonia and dimethyl ether vie OH, DME + NO ⇐⇒ R + HNO and RO₂ + NO ⇐⇒ RO + NO₂. For dimethyl ether/ammonia diffusion hot flame, the high temperature reactivity of dimethyl ether is improved by the reaction of OH, H and O radicals generated by ammonia with dimethyl ether and the reaction of HCCO + NO ⇐⇒ HCNO + CO and HCCO + NO ⇐⇒ HCN + CO₂. Moreover, this research shows that the main oxynitrides in dimethyl ether/ammonia cold flame and hot flame are NO₂ and NO respectively.