China has undergone rapid economic growth and diet transition over the past decades, along with environmental challenges. To help to achieve carbon peaking by 2030, this study investigates the time-variable diet-related greenhouse gas emissions (GHGEs) from 2000 to 2020 and examines the responses of food demands and diet-related GHGEs to an increase in per capita income and animal-based food prices. Based on the Almost Ideal Demand System model, addressing the problem of the endogeneity of food expenditure, we estimate the demand elasticities for six food groups and analyze their changing trends with time. Then, we perform two projections. One is to project the impacts of income growth on food demands and diet-related GHGEs, taking into consideration dynamic income elasticities as per capita income increases; the other is to project the effects of an increase in prices of different animal-based foods on food demands and diet-related GHGEs. Our results reveal that diet-related agricultural GHGEs show a continued increase in the short term, but the increased effect tends to decline gradually. The dominant driver of increased diet-related GHGEs is the increased consumption of beef, mutton, and pork. However, an increase in prices of beef and mutton; pork; and poultry and eggs can reduce diet-related GHGEs, while a decrease in the prices of aquatic products can also deliver a significant decrease in GHGEs. The results imply that policymakers should take an interest in the environmental impacts of diet transition and promote a more sustainable diet structure.