Tony Aitken, 33, formerly of Melton Mowbray, lost control of his truck on 4 May and his son Luke was thrown from the vehicle.
The boy was celebrating his 12th birthday when he died at Langar Industrial Unit, in Nottinghamshire, police said.
He died later from injuries sustained when the truck fell on top of him.
The truck had three children in the front seat, despite the vehicle only being meant to hold two passengers, Nottingham Crown Court heard.
The other children in the vehicle, aged 12 and five, were treated in hospital for minor injuries.
Aitken pleaded guilty to driving whilst unfit and causing death by dangerous driving and was jailed for five-and-a-half years, Nottinghamshire Police said. He was also disqualified from driving for seven years.
A tipper truck driver has been jailed after the lorry he was driving rolled, killing his son.