A ban introduced by state legislators would ban possession, sale and distribution of shark fins used in a soup considered a delicacy.
The proposed ban would follow a similar measure enacted in Hawaii last year.
Oregon and Washington are also considering similar legislation.
Shark fins are used to create a luxury Chinese soup that can sell for as much as $40 a bowl.
Supporters of the ban say shark finning is a cruel practice.
Leila Monroe with the Natural Resources Defense Council (NRDC) said shark finning is cruel.
She said the practice involves slicing off the shark's fin off while the animal is still alive and then throwing the rest of the shark back in the sea to die.
"The number of sharks that are being consumed is just not sustainable and we want to have sharks for our children's children to see," said Monroe.
Two Northern California Assemblyman Paul Fong (D-Cupertino) and Jared Huffman, (D-San Rafael) introduced the legislation.
If successful, the bill would ensure California ceases to be both a major supplier and consumer of shark fins.
The NRDC and other groups said every year people kill up to 73 million sharks for shark fin soup, a practice that is both wasteful and unsustainable.
"Many shark populations have collapsed worldwide due to overfishing, with some populations declining as much as 90-99 percent," said Brian Bovard with Defenders of Wildlife. "The IUCN Red List of Threatened Species has estimated that 30 percent of open ocean sharks are now threatened with extinction."
Bovard said previous laws in California still allowed finning but required fisherman to bring the entire shark carcass back to port, making it more difficult for fishermen to harvest fins.
"Because California remains a major import market, with San Diego and Los Angeles ranking among the top entry points for shark fin products, this legislation will have a significant impact," said Bovard.
The bill introduced today is supported by several groups including the Asian Pacific American Ocean Harmony Alliance, the Ocean Conservancy, Heal the Bay, Natural Resources Defense Council, California Coastkeeper Alliance, Defenders of Wildlife, Environment California, Monterey Bay Aquarium and Oceana.
