The charity Dogs Trust says there is a need for a "fundamental overhaul" of dog control laws to bring down the number of attacks.
There is also mounting pressure from MSPs.
It came after two young children in the west of Scotland were injured by dogs and needed surgery just days apart.
A five-year-old boy was bitten by a dog in Renton, West Dunbartonshire, on Tuesday, and a three-year-old was savaged by a pit bull a week before in the garden of a house in Kilmarnock.
As we reported, the five-year-old was due to undergo surgery for facial injuries, while the toddler is recovering following surgery.
Dogs Trust's Glasgow centre is urging people to educate themselves on the behaviour of the dogs to look out for signs.
A spokeswoman from the charity said: "Dogs Trust believes that there is a need for a fundamental overhaul of dog legislation."
She said the charity believed that legislation for protection from out-of-control dogs was "inherently flawed and should be repealed".
She added: "Breed-specific legislation is clearly not effective, and has done nothing to reduce the number of dog attacks since its introduction in 1991."
The Control of Dogs (Scotland) Act 2010 makes it a criminal offence to allow any dog to be dangerously out of control in any place.
Earlier this year Glasgow Provan MSP Paul Martin issued to plea to toughen controls and suggested all dangerous dogs should be muzzled.
He said: "I don't think we should be ruling out anything - this is a problem that won't go away.
"There has been some horrific attacks. It's also about dog owners being responsible."
Figures show there were more than 1000 reports of attacks by dogs last year in Scotland and an increase of 17% since 2010.
Lisa McGuiness, Dogs Trust Glasgow's Training and Behaviour Advisor, warned people to look out for signs.
She said: "People tend to say their dog snapped out of the blue but that's quite rare. Usually dogs display several signs that show they're distressed, unsure or in pain.
"Dogs might lick their lips, put their tongue in a different position, their body in a different position, or their ears."
A Police Scotland spokeswoman said anyone who has concerns about dangerous dog incidents should contact them for advice on 101.