Dazhong, the city's largest taxi company, won't carry students in cabs whose license plate ends in the number four, which is pronounced in the Shanghai dialect the same as the word "failure."
Many Chinese avoid four because it is pronounced the same as "death" in widely spoken Mandarin.
"Lots of parents refuse to take cabs with number plates which they consider unlucky," the Shanghai Youth Daily on Monday quoted Dazhong's taxi boss Zhao Leping as saying.
"We've seen many of them get angry at us because we have used them to carry their children in past years," Zhao said.
About 130,000 students will take the crucial three-day entrance exam starting Tuesday, and 20,000 cabs have been booked to deliver them to the tests on time.