Fresh produce such as carrots, tomatoes and apples will be sold loose in boxes without trays or clingfilm, which Asda hopes will recreate the look and feel of a traditional greengrocer shop.
Only delicate fruits such as raspberries that require packaging to protect them will remain packed, alongside a small number of convenience products.
Prices per kg will remain the same, however, while information about provenance will be flagged up on shelf barkers.
"We believe this return to traditional values could have a huge impact upon the amount of packaging thrown away every day," said buying produce manager Emma Sinclair-Morris. "Reducing packaging is one of Asda's key objectives, and we are considering every option to achieve this."
If the trial is successful, the scheme will be rolled out to every Asda store across the UK. "We believe our customers would prefer to shop in this traditional way if it means reducing waste and protecting our environment," added Sinclair-Morris. "Some fragile items of fresh produce, such as strawberries and raspberries, will always require some degree of packaging for protection, but most items can be sold loose but still preserve their high quality.
"This study will enable us to see if it is possible to encourage our customers to shop in a different manner to keep waste - and costs - to a minimum," she said.
Pre-packed fruit and veg accounts for up to 60% of all fresh produce sold by most major supermarkets in the UK, she said. Retail experts suspect many pre-packed items of fruit and veg are bought through habit as much as convenience.