Using molecular dynamics simulations, the adsorption and diffusion of doxorubicin drug molecules in boron nitride nanotubes are investigated. The interaction between doxorubicin and the nanotube is governed by van der Waals attraction. We find strong adsorption of doxorubicin to the wall for narrow nanotubes (radius of 9 Å). For larger radii (12 and 15 Å), the adsorption energy decreases, while the diffusion coefficient of doxorubicin increases. It does, however, not reach the values of pure water, as adsorption events still hinder the doxorubicin mobility. It is concluded that nanotubes wider than around 4 nm diameter can serve as efficient drug containers for targeted drug delivery of doxorubicin in cancer chemotherapy.