After Barkley, Kiper ranked NC State defensive end Bradley Chubb second, Georgia linebacker Roquan Smith third, Notre Dame guard Quenton Nelson fourth and Wyoming quarterback Josh Allen fifth.
The only difference in the top five compared to Kiper's previous big board was Smith and Nelson swapped spots.
After a highly productive collegiate career at Penn State, Barkley entered the predraft process with plenty of hype.
He racked up 1,903 yards from scrimmage and 23 total touchdowns last season, including two scores as a return man.
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Barkley then turned in a dominant performance at the NFL Scouting Combine, and he has done little to disprove the notion he's the best all-around player in the 2018 class.
Bleacher Report's Matt Miller is among the many who agree with Kiper in that regard, as he also ranked Barkley No. 1 on his most recent big board.
Although much of the focus has been on Barkley and a group of quarterbacks that includes Allen, Sam Darnold, Josh Rosen and Baker Mayfield, Chubb has a chance to be one of the draft's most impactful players.
After posting 10.0 sacks in each of the past two seasons at NC State, Chubb is the top pass-rusher in the class.
Similar statements can be made for Smith and Nelson, who are widely regarded as the best linebacker and offensive lineman, respectively.
The most heated debate throughout the draft process has related to the quarterback position.
Kiper believes Allen stands out, and ESPN's Todd McShay reported Monday he has heard from NFL general managers that the Browns want either Allen or Darnold with the No. 1 overall pick.
Miller has Darnold going No. 1, with Allen going No. 3 to the Jets, and his top overall player, Barkley, going No. 4 to the Browns.