The incident happened on Saturday around 8:40 p.m. at a Stater Bros. parking lot on the 16000 block of West Lakeshore Drive.
Police said the suspect walked up to the victim as she got to her car and tried grabbing her purse.
The purse was around the victim's shoulder, so she fell to the ground. She was dragged about 12 feet before the suspect was able to get the purse.
The suspect fled the scene in a dark-colored, 1990s model, four-door Honda.
The suspect was described as a dark-skinned male adult, about 24 years old, 5 feet 10 inches tall and weighing 160 to 190 pounds. He was wearing a black hooded sweatshirt, white T-shirt and blue jeans.
Anyone with information was asked to contact the Lake Elsinore Police Department at (951) 245-3300.