A surge in demand for shark fins, mostly for soup in Asia, has threatened various species of the predators, which have a vital role in maintaining the balance of marine ecosystems.
The ban, proposed a year ago by the European Commission, would forbid shark finning by all vessels in EU waters and by all EU-registered vessels operating anywhere in the world.
About one-third of all shark species are threatened with extinction, according to the International Union for Conservation of Nature.
Sharks are particularly vulnerable to over-fishing because of their slow growth rate and small number of young.
The appetite for their fins, which can sell for up to 1,000 euros ($1,300) each, is greatest in China, where they are the main ingredient of shark fin soup.
Thursday's European Parliament vote is a strong signal, but needs to be matched by approval from member states to make the draft law definitive.
European Commissioner for Maritime Affairs and Fisheries Maria Damanaki welcomed the step and urged swift agreement on "a real ban to shark finning without any derogations".
The proposed law would close a loophole in EU rules, which as they stand ban finning, but allow fishermen with special permits to land shark bodies and their more valuable fins at different ports - provided they comply with a fin-to-carcass limit of 5 percent.
Shark conservation groups have campaigned for years against the EU ratio, saying it is among the most lenient globally and allows European fishermen to dump large numbers of finned carcasses at sea each year.
Spain and Portugal are the only EU member states still issuing the finning permits.
Thursday's vote was "definitely a very positive step", said Sandrine Polti, policy adviser to the Shark Alliance, adding the group would continue to campaign for better management of depleted shark stocks.
Under the proposals, fishermen would have to land all sharks with their fins attached, although they would be allowed to slice partly through each fin and fold it against the carcass, to facilitate storage and handling.
