The dynamics for the collision of BH with He is investigated based on the CCSD(T) potential energy surface. State-to-state differential, partial and integral cross sections are calculated for the first time. The effects of the long-range attractive and the short-range anisotropic interactions on inelastic scattering dynamics are also discussed in detail. As a result, the nearly-linear collision of He atom from H atom side with the BH molecules is the most effective manner for j=0→j'=1.Furthermore, it is of advantage for the Δj=1 transition at lower energy and for the Δj=2 transition at higher energy. The state-to-state integral cross section displays a pronounced oscillatory structure. The long-range partial cross section has only an effect on the integral cross section for j=0→j'=1, and the cross sections for j'≥3 are almost determined by the anisotropic short-rang partial.