The rocker explained that he gets nervous when Jack, who stars in Adrenaline Junkie, takes part in extreme challenges.
According to Contactmusic, Osbourne said that he often fears he will get a phonecall saying Jack has died and added that his son has gone "crazy".
"He's got more f**king guns than the Army," he said. "My job is to point out what can happen. Jack goes bungee-jumping, skydiving. I mean, even the guys who invented skydiving all f**king died - while skydiving!
"He told me he wants to bungee-jump off a helicopter, over an active volcano."
Osbourne added that he is also concerned that Jack has replaced an addiction to drink and drugs with an addiction to extreme sports.
"He needed help and went into rehab," he explained. "So he's stopped all that. And now he's skydiving instead. What can I do?"
> Ozzy Osbourne: 'I can't stop worrying'