The scattering and absorption of raindrops will seriously increase the transmission loss of terahertz waves in the earth-space links and reduce the performance of wireless communications. In order to realize the transmission application of terahertz waves in the earth-space links, it is necessary to deeply study the transmission characteristics of terahertz waves in the rainfall environment. In this paper, the original rain attenuation model is further modified, and the influence of rainfall rate on terahertz wave transmission over the earth-space links is analyzed based on Mie theory. The calculation results are compared with that of the original model, and it shows that, in the whole terahertz bands, the rain attenuation loss increases with the increase of rainfall rate, and increases first and then decreases with the increase of frequency. There exists less rain attenuation loss in the high-frequency terahertz bands than in 0.1~1 THz bands. When the frequency exceeds 1 THz, the closer the atmospheric window is to 10 THz, the smaller the loss will be, and it will have more advantages in wireless communication transmission in rainy weather environment. The lower the frequency, the greater the zenith angle, and the difference of the rain attenuation model before and after modification will be more obvious.