  The oscillator strengths of the $H^+_2$ molecular ion,
$1s\sigma_{g}-2p\sigma_{u}$, $1s\sigma_{g}-2p\pi_{u}$ are calculated within the
Born-Oppenheimer approximation. The variational expansion with randomly chosen
exponents has been used for numerical studies. The oscillator strengths
obtained for the transitions $1s\sigma_{g}-2p\sigma_{u}$,
$1s\sigma_{g}-2p\pi_{u}$ of $H^+_2$ are accurate up to ten significant digits.
Results are given for the internuclear distances between 0.10 and 20.0 a.u.
