The 24-year-old's smart hooked volley for the second in Saturday's 2-0 win over QPR was his eighth of the season but his sixth in 13 Premier League starts.
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."
Everton face Arsenal at the Emirates Stadium tonight looking to end a miserable run at the venue and keep in the hunt for Champions League qualification.
Victory on Saturday took their tally to 13 points out of a possible 15 and they are only four points behind their third-placed opponents.
The Toffees have not won at the Emirates since the Gunners moved there in 2006, taking just two points from six visits.
Moyes is hopeful their recent good form can bring an end to that poor record.
"I think the squad are in good order, they have gained confidence from their results and the way they are playing," he added.
"This time of the season the games are hard because everyone needs the points for different reasons.
"We have got some momentum but we've got some hard games coming up so we've got to be ready for that but hopefully the bit of confidence we've got will help us."