The May figure compares to a revised 6.1 percent in April, and 7.3 percent in May 2013, according to the EDD.
The agency said the unemployment rate in California last month was 7.1 percent, and it was 6.1 percent in the U.S. as a whole. Neither the state nor national figures were seasonally adjusted.
The most job gains in May were seen in accommodations and food services, which picked up 3,200 jobs.
Over the past year, the sector added 4,500 positions. The financial activities area lost 1,000 jobs since May 2013.
Just over 92,000 San Diegans were without work last month from a workforce of almost 1.6 million. The total amount of people without jobs is more than 23,000 less than the same period last year, according to the state agency.