The grocer said it believes a new management regime should replace the CFP in an effort to give fishermen a stake in managing the stocks on which their livelihoods depend.
Asda chief executive Andy Bond last week unveiled plans to host a sustainability conference for Asda and rival retailers to discuss packaging and renewable energy. The retailer has also recently appointed former Asda agriculture and development manager Chris Brown to the newly created post of head of ethical and sustainable sourcing.
Asda regulatory affairs manager Gordon Maddan said: 'We want all the fish we sell to be sustainable. It's very clear, however, that the Common Fisheries Policy has failed to deliver this so we are now supporting calls for a radical change in approach.'
He added: 'We believe independent certification is the only way to secure the long term future of Scottish fisheries. We're already working closely with the Scottish Executive, Scottish Fishermen's organisations and the Marine Stewardship Council to try and bring this about.'
Today, the retailer also unveiled plans to call for the North Sea to be declared a marine conservation zone to preserve fish stocks for local fishing communities.
Earlier this year, Asda revealed it was changing the way it sources fish, bringing its sustainable fish policy into line with its parent company Wal-Mart. Within the next three to five years, Asda has pledged to only stock wild-caught fresh and frozen fish from fisheries that meet the Marine Stewardship Council's (MSC) independent environmental standard for sustainable and well-managed fisheries.