  {\it Ab initio} calculations within density functional theory with
generalized gradient approximation have been performed to study the effects of
oxygen vacancies on the electronic structure and magnetism in undoped
V$_2$O$_{5-x}$ ($0 < x < 0.5$). It is found that the introduction of oxygen
vacancies would induce ferromagnetism in V$_2$O$_{5-x}$ with the magnetization
being proportional to the O vacancy concentration $x$. The calculated
electronic structure reveals that the valence electrons released by the
introduction of oxygen vacancies would occupy mainly the neighboring V
$d_{xy}$-dominant band which then becomes spin-polarized due to intra-atomic
exchange interaction, thereby giving rise to the half-metallic ferromagnetism.
