With former first-choice Nikica Jelavic enduring a drought, with just one league goal since December 8, Anichebe's all-round form has provided a welcome boost as the Toffees retain hopes of a top-four finish.
"I think he has a bit more to do but we have got signs of someone who could be an outstanding player," said Moyes.
"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.
"He has been terrific. 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.
"We just want him to keep playing the way he is doing; he is helping us at the moment and gives us an alternative. I think for Everton we need people who are getting in double figures (for goalscoring).
"We've really missed someone getting in the high teens with their goals. I hope he gets some more because it will help us until the end of the season."