The Standardized Precipitation Evapotranspiration Index (SPEI) has been widely applied, due to its multi-scalar features and the ability to identify different drought types. However, its sensitivity to climatic variables still remains unclear, especially at different time scales. Therefore, this study investigates the sensitivity of SPEI to average temperature (Tmean), diurnal temperature ranges (Tdelta), relative humidity (RH), solar radiation (Rs), wind speed (U2), geothermal flux (G), and precipitation (P) from 1957 to 2017 using the extended Fourier Amplitude Sensitivity Test at different time scales in Jilin Province, China. Jilin Province experienced a significant rise in Tmean, and a sharp decrease in Tdelta, Rs, and U2. P is undoubtedly the most influential factor to the SPEI among the meteorological variables, which explained 59.9%–97.9% of the total variability, especially during the main crop growing season (from May to September). While Tmean, RH, or U2 observably affect the SPEI and cannot be neglected during the nongrowing season. In terms of spatial distribution, the SPEI was mainly affected by P in the eastern region, while it was also influenced by Tmean, RH, and U2 as well in the western region. The sensitivity of the SPEI differs in time scales: P > Tmean > RH > U2 > Rs > G > Tdelta (1 to 6 month), P > U2 > RH ≈ Tmean > G > Rs > Tdelta (7 to 18 month), and P > U2 > G > Tmean > RH > Rs > Tdelta (more than 24 month time scale), respectively. The results have the potential to provide a reference for agricultural production and management in Jilin Province, China.