Cataracts are a clouding of the lens in the eye that affects vision, and are very common in older age.
The hospital says the overdoses were caused by an incorrect setting on a CT scan machine.
The hospital says about 20 percent of the 260 patients had radiation exposure to the lens of their eyes.
Hospital officials notified the affected patients by letter. They apologized to them and said the overdoses were "completely unacceptable."
They also offered to pay for the treatment of any subsequent health problem and make their staff available for any questions or concerns.
Cedars Sinai officials said they would continue to work with the USDA to help prevent the same situation at other hospitals in the future.