  We solve numerically a field equation of axions coupled with gravity and show
solutions representing oscillating axionic boson stars with small mass $\sim
10^{-12}M_{\odot}$ and large radius $\sim 10^{8}$ cm. We present explicitly a
relation between the mass and the radius of the boson stars with such a small
mass. These axionic boson stars are shown to possess oscillating electric
currents in an external magnetic field and to radiate electromagnetic fields
with a frequency given by mass of the axions. We estimate the luminosity of the
radiation in a strong magnetic field $10^{12}$G of neutron stars, typically
$\sim 10^{24}$ erg/s with the axion mass being $10^{-5}$eV.
