About half of ocean shark species and one-third of European sharks could become extinct if nothing is done, experts told the BBC. Oceana, a group campaigning for stronger regulation, said the rules are confusing and not enforced well.
Ted Danson, the U.S. actor who has become a spokesman for the campaign, said one of the big problems is that few commercial fishermen actually go out for shark. Most are caught along with marlin, swordfish and tuna.
"The basic problem is it's a fishery that's not even considered a fishery in most areas," Danson said.
In Europe, fishermen often remove the fins and then toss the rest of the shark back. Under EU rules, the fins cannot be more than 5 percent of the total weight of shark landed.
The United States has stricter regulations in the Pacific with fins allowed to be no more than the dressed weight -- minus bone and other inedible parts -- of landed sharks. U.S. rules for the Atlantic and Gulf of Mexico require all sharks to be landed whole, which experts say allows a reliable count to be made.