Jenny Dees, of Hull, started the petition after her son Stanley Metcalf, was shot dead by his great-grandfather Albert Grannon at the 78-year-old's home last summer.
Stanley's Law aims to educate people on the dangers of air weapons and change the licensing in England.
Under Stanley's Law, it would be an offence to use, possess or acquire an air weapon without a certificate in this country.
The petition is available to sign by clicking here.
The petition has now been signed by more than 8,500 people. A total of 10,000 signatures are needed for it to get a response from the Government.
Miss Dees said: "For me I feel so overwhelmed with all the love and support everyone is showing us.
"We’ve received some heartfelt messages from bereaved parents sharing their stories.
"We watch the signatures go up every minute and it makes me feel I’m not alone.
"I tell Stanley every night we are going to do this son but I can’t wait for the day when I can say we did this son."
Scotland and Northern Ireland have licensing laws, but in England and Wales you do not need a licence to own most air guns.
The power limit is set at a muzzle energy of 12ft.lb for air rifles and 6ft.lb for air pistols.
Miss Dees wants this to change following the death of Stanley, who was shot by Grannon, using a .22-calibre gun.
The pensioner, who was jailed last week for three years, had the weapon modified to make it more powerful, but did not apply for a licence thinking he would not get one because he was partially disabled.
Miss Dees said: "Even if the air weapon my granddad had wasn't modified we were told by an expert that it would have still killed Stanley.
"People say air weapons are not dangerous, but I have the proof they are as Stanley is dead as a result of one.
"Nothing we can do will bring Stanley back but if our campaign and petition stops just one person getting hurt or fatally injured it will be worth it."
A Home Office spokeswoman said: "We commenced a review into the regulation of air weapons in England and Wales in late 2017. This was to assess whether the current controls, which are already strong, continue to be appropriate and effective. We intend to publish our conclusions as soon as possible."