The man, who was in his 70s, was involved in the accident on the Ragley Hall Estate on Tuesday and suffered a number of serious injuries including a pelvic injury, West Midlands Ambulance Service said.
A spokesman said: "We were called to a road traffic accident at Ragley Hall in Alcester, Warwickshire, on Tuesday at 3.30pm to reports of a collision between a lorry and a pedestrian.
"The patient was airlifted to Queen Elizabeth Hospital in Birmingham. In attendance was one ambulance, a paramedic area support officer and two Midlands air ambulances. Warwickshire Police were called."
He died later in hospital.
Show organisers, who are known as the the APF Demo team, are said to be distressed and stunned but decided to continue the show as planned. In a statement, they said: "The APF Demo's team's thoughts are very much with the family at this time and it’s their wish that the APF Show continues."
The statement said the member of staff "received immediate first aid treatment by the on-site St John’s Ambulance staff and was subsequently flown to a Birmingham hospital for further treatment.
"Tragically despite the best efforts of the doctors he died around 7pm. Police attended the accident and are currently investigating. As this an ongoing investigation we will be not be comment further at this stage."
A Warwickshire Police spokeswoman said police were informed by the ambulance crew of the accident at 3.40pm on Tuesday and launched an investigation. As the incident was on private land and not a criminal investigation, it was passed on to Stratford District Council, which is now investigating. The Health and Safety Executive has also been informed.
The APF Show is owned by Confor, the membership organisation for the timber supply chain. This is the 42nd show with more than 300 exhibitors this year. The show website says of the event: "The APF 2016, the UK’s largest and most exciting forestry, woodland, arboricultural, trees and timber event will be the biggest and best event we have ever staged in our 42 year history. "
It adds: "The APF Demo is run by a small dedicated committee who, when not organising the exhibition, work, or have worked, for many years in the forest industry."