One of them, a fictional Second World War story, was read at the service.
Prime Minister John Key described him as a true hero who had died trying to rescue civilians under attack in Kabul.
One of his SAS comrades had rushed to his side when he was shot and tried to resuscitate him while under fire.
Corporal Grant's coffin arrived on a gun carriage pulled by a large four-wheeled vehicle with an SAS escort on the running board.
Engineers in a slow march escorted the procession. His coffin was draped in a New Zealand flag and carried his military medals and sword.
Corporal Grant was one of five sons, and one brother, Stuart, gave a moving eulogy about his brother . "We'll miss you mate."
He was a Triumph bike rider and a member of the Patriots Defence Forces Motorcycle Club.
The music at the funeral included Wild Horses by the Rolling Stones and Ride on by ACDC.
Corporal Grant, 41, was shot dead last week during an operation to rescue hostages at the British Council cultural centre in Kabul, the capital of Afghanistan, which was being attacked by the Taleban.
Eight policemen and three Afghan guards were also killed in the raid.
Corporal Grant left his wife and two children.
He will be cremated after a private family service in Palmerston North this afternoon.