The 51-year-old "Fury" star, who is a huge fan of the Bristol street artist, will view the new park in Weston-Super-Mare, South West England, away from the general public because he would "get mobbed", reported Daily Mirror.
"Brad has followed Banksy's work for years now and really loves his ideology, so he is making special arrangements to ensure he can get down to the park.
"Brad would bring a bit too much glamour to what's meant to be a thoroughly depressing visit, so Banksy granted him special permission to visit before it opens. Obviously such a high profile celebrity would get mobbed in Weston-super-Mare if he travelled down and queued with the public," a source said.
"Banksy has granted Brad special permission to visit the park before it opens to the public. The first tickets allow entry at 11am, so Brad will have the run of Dismaland in the morning before then during his visit next week.
"He's not planning to take Angelina and the kids." the source addded.