The Greenpeace report is called Carting Away the Oceans.
"For the first time, half of the leading supermarket chains in the U.S. received passing scores in the sustainability of their seafood operations. It is positive news, but we still have a long way to go," said Casson Trenor of Greenpeace.
Greenpeace is most impressed with local outlets that include Target, Whole Foods, Wal-Mart, Safeway and Trader Joe's. Target's No. 1 ranking is due in large part to a new purchasing policy that resulted in the removal of all farmed salmon products from their stores.
"We've got stores like Target which have made incredible positive decisions to do things like stop selling all forms of farm salmon," Trenor said.
Consumers say that list gives them a good idea of where to shop for more sustainable seafood.
"I do like that as a customer," a Target consumer said.
"I also try to pay attention to the ones that are endangered like Chilean sea bass and orange roughy and those," another consumer said.
Last month, Trader Joe's announced it is going to make moves to change its seafood policy, which moved the chain from the worst ranking up to the 10th spot on the Greenpeace scorecard.
On the Trader Joe's website, the company wrote: "In our efforts to offer seafood options that fit customer needs ranging from food safety and taste, to concern over the environment, we have established the following goal: all of our seafood purchases will shift to sustainable sources by December 31, 2012. This applies to all formats of seafood we offer: frozen, fresh, canned, etc."
"Food supply from the sea that we once considered unbounded is now bounded especially with toxins and such," consumer Ron Mitooka said.
Greenpeace gave low marks to Costco and Albertsons saying neither company has changed its seafood buying practices and those policies are harming the marine environment.
"If you are making millions and millions of dollars a year buying and selling fish, you need to take responsibility for the fact that you are having an impact on the ocean," Trenor said.
Greenpeace publishes its survey in order to raise awareness for consumers and put pressure on retailers to do better.
"The days of selling fish with no regard for the environment are over," said Tenor.
Aside from Target, Safeway was the only other chain to respond to ABC7's request for comment on the issue. They said they are proud of the steps they have taken in that arena, and they are looking for opportunities to do even more.