The Boltzmann-Uehling-Uhlenbeck (BUU) model, which includes the Fermi motion, the mean field, individual nucleon-nucleon (N-N) interactions and the Pauli blocking effect, etc., is used to calculate the total reaction cross section σ_R induced by α-particles on different targets in the incident energy range from 17.4 to 48.1 MeV/u. The calculation result can well reproduce the experimental data. The nucleus-nucleus interaction radius parameter r₀ was extracted from experimental σ_R. It is found that r₀ becomes constant with the increasing mass number of target.