Joshua is weeks away from the biggest fight of his career, against Wladimir Klitschko at the O2 Arena on April 29, but instead of waging war with the Ukrainian, he's replying to Fury's shots. Besides, Joshua has to prove still that he can beat 41-year-old past his best Wladimir Klitschko on April 29 at Wembley Stadium.
Fury, who transformed the world heavyweight picture when he became the first boxer in 11 years to defeat Klitschko in 2015, paving the way for former Olympic champion Joshua's shot at a title, countered by saying: "I might be fat, but you're a paper champ and paper-chinned weightlifting rudeboy, wannabe badman".
"Anthony Joshua is a poor man's Frank Bruno", he wrote.
And Fury, who had to vacate his titles past year, took to Twitter to swipe a shot at Joshua ahead of the fight.
"Typical @Tyson_Fury always tlking BS around fight time. Same offer as last time. x2 ringside tickets, don't bring a plus one - it's for your fat ass".
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"Looking great, very relaxed, and we're going to have 90 thousand at Wembley and I think Klitschko, just throwing out a few mind games now, I'm excited for fight week".
But he did hit back at Tyson Fury on social media. "I've been working very hard out here in CT in training camp so I'll be in great shape come fight night and I'm just really looking forward to it now and being part of such a historic event".
Joshua then appeared to lose patience with his heavyweight rival: "Shut up and give me a date when you'll be back!" Be about what you say.
Anthony Joshua has a U.S TV deal with Showtime which was agreed in May of 2016, which grants Showtime exclusive American TV rights to show Anthony's fights in the United States and other North American territories.
With Fury replying: "You shouldn't throw stones when you live in a glass house".