The van was carrying eight kindergarten pupils and two teachers, as well as the driver. It was meant to carry only seven people, according to Xinhua.
The crash happened in the late afternoon near the province's capital of Changsha, in a mountainous area.
Local media reported it was travelling on a narrow road that had no barrier.
The victims' family members told Xinhua that school buses in the region are often overloaded.
School transport is a particularly sensitive issue in China, where a series of accidents have heightened concern.
A shortage of education funds has seen school closures and children, especially those from rural villages, are often forced to travel far to get an education, according to agencies. They often have to take overcrowded buses.
In 2011, 18 children and two adults were killed when an overloaded school bus collided with a coal truck in foggy conditions. That bus had only nine seats but was packed with 64 people at the time of the accident.
The following year a school van plunged into a pond in Jiangxi killing 11 children, and three children on board a bus died in a traffic accident in Guangdong.
China's cabinet issued new rules governing school bus safety, setting out specifications for school buses and punishments for offences such as overloading.
An overloaded minivan ferrying children home from kindergarten in China's Hunan province has crashed into a pond, killing all 11 people on board.