This study aims to quantitatively analyze the impact of agricultural scientific and technological progress on rural economic growth. The contribution rate of agricultural scientific and technological progress in place A is measured through beyond logarithmic function model setting, data collection and processing. An agricultural carbon emission measurement model was built, in order to analyze the dynamic changes of total carbon emissions in place A. In addition, the gray correlation analysis algorithm was used to rank the correlation between agricultural science and technology indicators and economic growth in place A. Finally, a regression model is designed to analyze the impact of scientific and technological progress on rural economic growth. The coefficient of the t2 term of the contribution rate model of scientific and technological progress is 0.0013, which is greater than 0, indicating that there is scientific and technological progress in 2017-2023 in place A. The carbon emissions in place A decrease year by year with scientific and technological progress. All indicators in agricultural science and technology inputs can promote agricultural economic growth, and the gray correlation value in descending order is, T3>T9>T8>T1>T6>T4>T7>T2>T5. Scientific and technological progress has a different degree of promotion for the rural economic growth in place A.