Osbourne recently suggested that the 18-year-old will not "stand the test of time", explaining that he still looks like a "little boy".
However, Bieber now appears to have responded to Osbourne in a series of posts on his Twitter page.
He began by saying: "doubt me....i like it" before adding: "im working on something special".
Bieber than explicitly addressed Osbourne, posting a link to his latest music video 'Beauty And A Beat' along with the words: "Not worried sharon.."
Bieber and Nicki Minaj unveiled the video for 'Beauty And A Beat' last week after an elaborate publicity stunt in which Bieber claimed that his computer containing "personal footage" had been stolen.
Watch the video for 'Beauty And A Beat' below: