The Los Angeles Times reports the insurers want in excess of $230,000 from 14 crashes in the U.S.
The suits, which were filed in Los Angeles, claim negligence and fraud by Toyota.
Toyota has recalled more than 10 million vehicles since late 2009 and blames driver error, faulty floor mats and sticky accelerator pedals for the unintended acceleration.
Toyota says the lawsuits are without merit.
The Associated Press contributed to this report.