Kim Stanton from Young Driver said, according to The Mirror: "Driving a vehicle is potentially one of the most dangerous and responsible things a person can do.
"Learning to drive should be done over a long period of time and from a young age, when pupils are more receptive to safety messages."
Young Driver offers training that allows under 17s to get driving experience.
Stanton said Young Driver commissioned independent research that showed that drivers who have taken their courses before the age of 17 are half as likely to have a crash when they do pass their test.
Writing on the petition, Stanton claimed research shows a quarter of all 15 to 19-year-olds who die are killed in cars.
Research from the RAC foundation in May 2015 also found one in five young drivers will crash within the first six months of passing their test.
The RAC also found teenage drivers make up just 1.5% of full licence holders, but are involved in 12% of serious road traffic accidents where someone is seriously injured or killed.
At the time, Melanie Williams, a senior serious injury solicitor based in Thompsons Solicitors’ London office, said: "Countries across Europe have trialled and introduced graduated or phased driving tests for young drivers, providing them with the opportunity to develop skills and experience over a longer period of time.
"Given the seriousness of these figures, the UK now needs to explore the benefits of an alternative driving licence system and new ways of testing in a bid to reduce the number of needless deaths on our roads."
Mark Lewis, director of standards for the Institute of Advanced Motorists (IAM), said about the petition, according to The Express: "The high number of accidents and the sad loss of life as a result of unprepared young drivers urgently needs to be tackled.
"That’s why I strongly believe people should sign this petition and get the subject debated in the House of Commons."
The petition needs 10,000 signatures to get a response from the government and 100,000 signatures to be considered for debate in parliament.
Kim Jones enrolled her 14-year-old son in a driving lesson in August 2014.
"I haven't seen Steffan concentrate this hard since he was last on his X-box. And he's taking instructions and acting on them, without answering back, deferring with a 'yeah, yeah, I'll do it later,' or totally ignoring commands.
"At the end of our lesson, I'm convinced that these sort of pre-learning skills should be available to all young drivers. Maybe even as part of the school curriculum. But that, of course will cost money."
Blogging on HuffPost UK Parents Drew Hendricks said parents can help prepare their children for learning to drive by letting them get behind the wheel while they're young.
"There are some things you can't simply act out - proper mechanical and legal maintenance of the vehicle, for example," he wrote.
"Whoever is behind the wheel, whether it's you or your teenager, communication is key. If you're driving on your own, think of how you could explain the things that you're doing, and what you're keeping in mind, if your child were in the car with you."
To sign the petition or to find out more, visit the petition here.