The hikes, which will average about 15 percent, take effect on Sunday and is slated to affect 120,000 policy holders.
The increases come despite objections from a state regulator.
A spokesperson for the California Department of Managed Health Care said it requested Anthem Blue Cross lower its rates.
This marks the first time the regulator has branded a rate unreasonable.
In a statement, Anthem spokeswoman Kristin Binns said the regulator appeared to have changed its mind from a March 3 assessment that found the increase was not unreasonable or unjustified.