The Gloucester number eight will lead an England XV featuring five uncapped players, including Exeter's Tom Johnson and Sale's Carl Fearns who start alongside him in an inexperienced back row.
Narraway goes head-to-head with the Italy captain Sergio Parisse while Toulon flankers Joe Van Niekerk and George Smith complete a Barbarians back row that would match any in the world.
"It's not bad, is it?" said Narraway, who is battling for a place in England's World Cup training squad.
"If we're talking about a game where people want to prove themselves, prove how well they're playing and their form, in the back-row you're not going to come up against much better.
"So if you can perform against Parisse, Van Niekerk and Smith then I'm sure you can perform against any back row in the world.
"They have quality players throughout but we've got a very exciting player in Tom Johnson who has taken the Premiership by storm. He got my vote for player of the season.
"It will be great to play alongside him and see how he goes and then we've got a very abrasive player in Carl Fearns.
"We're not going to take a step backwards, we're going to get in the mix and see how we get on."
Harlequins prop Joe Marler and Worcester lock Graham Kitchener are the other uncapped players in the England pack, while Narraway's Gloucester team-mate Henry Trinder has been named at outside centre.
Two players leaving Kingsholm this summer, the prop Paul Doran-Jones and lock Dave Attwood, are both live World Cup contenders and have a point to prove this weekend.
Ugo Monye and James Simpson-Daniel start on the wings and Mike Brown gets a run at full-back after an impressive season for Harlequins.
Matt Banahan can be confident of a place in Martin Johnson's World Cup plans but England are using this game as an opportunity to try him out at inside centre.
"Within the squad everyone's got their own ambitions, whether that's Henry Trinder coming in for the very first time trying to make an impression and feeling very excited, or whether it's myself or Simpson-Daniel or Ugo who are fighting tooth and nail to try to get into the World Cup squad," said Narraway.
"Everyone knows what's on the line and while that's an underlying tone, this week is all about the Barbarians.
"It's about performing well so everyone can have an opportunity to show how good they are."
Narraway enjoyed an impressive introduction to Test rugby and was one of England's standout players on an otherwise disappointing tour of New Zealand in 2008.
But his star fell swiftly. Narraway was injured for the autumn internationals in 2008 and then failed a fitness test at the start of 2009.
By the end of that season he was out of the international picture and only now has he come back into focus at a time when England need back-up for first choice number eight Nick Easter.
James Haskell has played for England across the back row while Chris Robshaw and the newly-qualified Thomas Waldrom are competing with Narraway.
"It has been frustrating," said Narraway.
"I'd be lying if I said I wasn't disappointed (as other players got picked ahead of me) but that's the professional game.
"If someone's got a gran that's English, then they've got an opportunity to play for England, and that's the way it is, and that's fine.
"I went off the boil a little bit after that tour and then I backed that up with a season where I was injured and only played five games.
"I kind of fell off the radar but I feel I've had a decent season and Sunday's a great day to get myself back into the shop window and hopefully show what I can do."
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