Morrisons is to introduce paper bags costing 20p as part of an eight-week trial.
At the same time, the supermarket will increase the price of a plastic 'bag-for-life' to 15p.
The trial, across eight stores, is in response to customers saying that reducing plastic is their top environmental concern, Morrisons said.
The supermarket removed 5p carrier bags early in 2018 which led to a 25% reduction in overall bag sales.
The new US-style paper grocery bags have handles and are a similar capacity to standard plastic carrier bags.
Morrisons said the stores participating in the trial are Camden, Skipton, Wood Green, Hunslet, Yeadon, Erskine, Gibraltar and Abergavenny.
The 5p plastic bag levy was introduced in England from October 5 2015 and all large retailers have been required to introduce the charge. Similar schemes run in Wales, Scotland and Northern Ireland.
Environment Secretary Michael Gove has set up a consultation exercise that ends next month on raising the fee to 10p and including smaller retailers, which could come into effect from January 2020.
Retailers are expected to donate any proceeds from the 5p charge to good causes.
Figures from the Government at the end of 2018 showed that nearly two billion 5p plastic bags were sold in the last financial year.
This is a stark reduction from 2014, when 7.6 billion carrier bags – the equivalent of 140 per person – were handed out solely by England’s seven largest supermarkets.
Figures from the Department for Environment, Food and Rural Affairs (Defra) show the same seven retailers – Asda, Marks and Spencer, Sainsbury, Tesco, The Co-operative Group, Waitrose and Morrisons – sold 1.04 billion bags in 2017/18, nearly 60% of the 1.75 billion in England.