The backscatter from precipitation particles observed by the vertically pointed antenna beam of the Chung-Li VHF radar and the drop size distri- butions measured by a ground-based disdrometer co-located at the radar site are analyzed and studied in this article. We find that the disdrometer- measured drop size distribution can be well approximated to a Gamma distribution. On the basis of this property and a power law approximation to the fallspeed-diameter relation V_D = AD^B, we derive the theoretical re- lation between terminal velocity V_D and range-corrected VHF backscatter P of the precipitation particles. We find that theV_D - P relation follows a power law in the form of V_D = αP^β, where α and β are both the functions of the precipitation parameters. Chu et al. (1999) first found that the rela- tion between α and β  can be empirically approximated to an exponential form of α = Ae^ξβ, where β is a function of B and ξ is a factor associated with precipitation. In this article, under the assumptions of the Gamma distribution of the drop size distribution and the power-law relation between V_D and D, we theoretically show that the analytical relation between α and β indeed follows an exponential form of α = Ae^ξβ, where ξ is a function of the drop size distribution. The experimental results obtained by the Chung-Li VHF radar combined with the ground-based disdrometer measurements validate the exponential approximation to the α - β relation. The uses of the α - β relation for the investigations of the rainfall rate and properties of drop size distribution are presented and discussed.