Marie Wade and her two-year-old son Joshua were terrified when a "scary" bull terrier dog came hurtling towards them as they enjoyed a sunny afternoon in Ashton Gardens on Tuesday.
Marie, 33, has called on owners to be more responsible in such public places to prevent "an accident waiting to happen".
She said: "We were feeding the squirrels, my little one was with me running around.
"This man threw a ball for his dog and it just came running past us and back over to us and scared the little one."
She added: "I felt a bit shaken up about it, but upset really that they are allowed to do that, because it is an accident waiting to happen."
Marie said she told the man the dog should be on a lead. She said he rudely replied: "Your child should be on a lead".
Marie continued: "I go there every day when it's nice weather. The three people I saw with dogs, only one was on a lead."
"It was intimidating. It frightens me a dog like that can be near my child."
A Fylde Council spokesperson said: "As with many other parks in the borough, dogs being walked in Ashton Gardens should be kept on a lead in order for owners to maintain control of the animal.
"In all cases dogs, especially ones that can be intimidating, should be kept under control when around vulnerable people such as children and the elderly.
"If anyone experiences an incident where they consider an animal to be improperly controlled in one of our parks they can report the incident to the park office, such as the one in Ashton Gardens, who will then call the dog warden to attend and deal with the incident."