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The oscillator strengths of the $H^+_2$ molecular ion,$1s\sigma_{g}-2p\sigma_{u}$, $1s\sigma_{g}-2p\pi_{u}$ are calculated within theBorn-Oppenheimer approximation. The variational expansion with randomly chosenexponents has been used for numerical studies. The oscillator strengthsobtained 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.

The Oscillator Strengths of H2+, 1s\sigma_{g}-2p\sigma_{u}, 1s\sigma_{g}-2p\pi_{u}