Following a review of suppliers' sustainability plans a number of core John West lines will be de-listed by the end of July.
Tesco plans to work with John West on its remaining lines to convert them to sustainable tuna sources as soon as possible.
"We are proud of the progress we have made so far, and are committed to continuing to work in partnership with John West, other brands and our NGO partners to do everything we can to make high-quality, sustainable fish available for our customers," said Tim Smith, Tesco Group Quality Director.