The 68-year-old, identified only by her last name Cha, has taken the test almost every working day since 2005 in the southwestern city of Jeonju. She failed again on Monday for the 771st time.
"It was a record-breaking number here," Choi Yong-Cheol, a police sergeant supervising the test in the city's Deokjingu district, told AFP.
"I wonder if she will try it again for a 772nd time."
The Korea Times said Cha will in fact be back for another attempt.
Choi said that Cha cannot pass the preliminary written section of the test, averaging scores of 30-50 whereas the pass mark is 60 out of 100.
Local media said that Cha sells food and household items door-to-door at apartment complexes, carrying the items in a handcart, but wants to get a car for her business.
Police estimate she has spent almost five million won to take the written test, with each test costing 6,000 won (£3) in addition to other expenses.
"I feel sorry every time I see Cha fail. When she passes, I'll make a commemorative tablet myself and give it to her," one officer was quoted as saying.
