George Sim, 25, from Possilpark, was arrested after dumping the weapon in bushes at Springfield Quay in January.
He was followed after meeting his ex-girlfriend at the nearby Ibis Hotel where staff became suspicious that he was armed.
At the High Court in Glasgow, Sim admitted charges under the Firearms Act. Sentence was deferred and he was remanded in custody.
A man is facing a prison term for possessing a pistol in Glasgow.