Aldi will encourage customers to buy reusable or compostable bags instead of plastic versions.
From July, Aldi stores with offer either paper or compostable carrier bags at all its supermarkets The most popular choice will then be rolled out nationwide.
In the North East, Aldi will introduce compostable versions, although plastic will still be available.
Aldi says the option which is picked could save up to 1,300 tonnes of plastic a year, or 33.3 million carrier bags.
The supermarket's compostable bags are made of Bioplast, a material which is designed to be break down within 12 months.
Shoppers will pay 6p for the biodegradable bags.
The paper carriers will cost 19p each at the check out.
Fritz Walleczek, managing director of corporate responsibly at Aldi, said: "Reducing the amount of plastic we produce is fundamental to our commitment to being a sustainable and environmentally responsible business. This trial will identify the option which best suits our shoppers.
"Cutting waste is part of Aldi’s DNA and we are constantly looking for new ways to reduce our environmental impact. This new trial is one of the biggest we have ever launched because we want our customers to be involved and help us make the right decision for them and the environment."
Alongside the trial, Aldi has also set out a pledge to reduce plastic packaging by 25% by the end of 2023.
Last week, Sainsbury's pledged to get .
