The Everton boss admits the Nigerian's recent performances have been terrific and hopes he can finally kick on and develop into one of the Premier League's top strikers
Anichebe netted the second goal in the Toffees' 2-0 win over QPR on Saturday, his sixth goal in 13 Premier League starts.
And Moyes admits the 24-year-old’s form has been vital in his side's push for the top four, with the misfiring Nikita Jelavic scoring just once since the beginning of December.
He has been terrific," said Moyes. "The boy has an awful lot going for him and I've said many times he's just needed to have a bit more self-confidence.
"I think he has a bit more to do but we have got signs of someone who could be an outstanding player.
"It has taken a while for him to show us that but how he has been playing is very good and is playing as well as anyone - but we needed it because we've been a bit short there."