Barrow, 30, captained the Heed as they almost gained a play-off place in the National League.
After penning a new one-year deal as Mike Williamson plots a promotion bid in 2019/20.
“It’s a sad thing that we’ve been relegated," he told the club's website.
"But we’ve got to use that as motivation and get ourselves back up at the first time of asking.
“I love this club, it was obviously a tough one when we got relegated and for me I want to play at the highest standard I can.
"We’ve got unfinished business,” he added.
Gateshead get their National League North season underway against Southport on August 3.
You can view a full list of Gateshead's fixtures by clicking here.