"I'm really angry about it. I hike in the park all the time with my dogs and it poses a potential life-threatening danger to me," said David Klar, a park visitor.
Los Angeles City Councilman Tom LaBonge said all the fires have one thing in common: they were set by the roadside.
The fires erupted around noon near the Travel Town museum on Saturday.
"Because it's accessibility to the Ventura Freeway, it does cause concern that someone is jumping off that freeway running up to the park," said LaBonge
The fires come after two others on July 28 and August 4. Officials are not sure if they are connected.
The conditions at Griffith Park are very dry. Officials worry a fire could roar out of control and become extremely dangerous.
Those enjoying the park have said they are upset someone would intentionally set out to destroy the area.
"It's bad and, well, it's a beautiful park and I don't want anybody to ruin it. And, it's really kind of mean because it's also destroying a plant's life," said Nicole Klar, a park visitor.
Officials have considered restricting access to certain areas of the park. LaBonge hopes to avoid that option. Instead, LaBonge has said he'd like to meet with hikers, workers and park regulars to encourage them to watch out for suspicious activity.
"This is an active crime. A firefighter was hurt in this fire over the weekend and that was a deliberate act of arson that they believe it is. So, we want people to be able to call ... be aware of it," said LaBonge.
Officials say the arsonist could have been disguised as a bicyclist or a hiker so he or she would go unnoticed.
Anyone with information, anyone with anything that looks suspicious should call 911.