When axion stars fly through an astrophysical magnetic background, the axion-to-photon conversion may generate a large electromagnetic radiation power. After including the interference effects of the spacially-extended axion-star source and the macroscopic medium effects, we estimate the radiation power when an axion star meets a neutron star. For a dense axion star with $10^{-13}\,M_\odot$, the radiated power is at the order of $10^{11}\,\mbox{W}\times(100\,��\mbox{eV}/m_a)^4\,(B/10^{10}\,\mbox{Gauss})^2$ with $m_a$ as the axion particle mass and $B$ the strength of the neutron star magnetic field. For axion stars occupy a large fraction of dark matter energy density, this encounter event with a transient $\mathcal{O}(0.1\,\mbox{s})$ radio signal may happen in our galaxy with the averaged source distance of one kiloparsec. The predicted spectral flux density is at the order of $��$Jy for a neutron star with $B\sim 10^{13}$ Gauss. The existing Arecibo, GBT, JVLA and FAST and the ongoing SKA radio telescopes have excellent discovery potential of dense axion stars.

16 pages, 2 figures