Morrisons is hiking the price of long-life plastic bags to 15p and introducing a paper version costing 20p as part of a pilot scheme.
The supermarket said the eight-week trial at eight stores is in response to customers saying that reducing plastic is their top environmental concern.
Morrisons removed 5p carrier bags early in 2018 which led to a 25% reduction in overall bag sales.
The new US-style paper grocery bags, priced at 20p, have handles and are a similar capacity to standard plastic carrier bags.
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.