Arthur MacVean, 63, is alleged to have driven along at speeds of up to 65mph in a 30mph area, and collided with a wall in Danes Drive, Scotstoun, before hitting David Young.
MacVean told the High Court in Glasgow that he braked using both the foot brake and handbrake and also put the Vauxhall Vectra into neutral, but said that nothing slowed it down.
He said that as he approached the junction with Victoria Drive the car sped up and added: “It seemed to get faster.
“I remember the car going very, very fast. It seemed to gain speed quite dramatically. I looked down briefly to see if the accelerator was struck down by a floor mat, but it wasn’t.”
The court heard that MacVean, of Northland Drive, Glasgow, had been returning from a trip to the shops at 4:25pm, when the accident happened.
MacVean claimed he had put the car into neutral and it had had no effect. He said: “The car did not respond to what I wanted to do with it.
“I was battling to control the car. It was a very dangerous situation I was in.
“My foot wasn’t on the accelerator. My feet were on the clutch and brake.”
MacVean was asked by prosecutor Jamie Gilchrist QC if he had made up a story about there being something wrong with the car to explain what happened and he replied: “It’s not something I would invent.”
Mr Gilchrist then said: “Are you sure there was something wrong with the car?” and MacVean replied: “Yes.”
MacVean denies causing the death of Mr Young by driving dangerously at speeds in excess of 65mph, overtaking a car stopped at a red light, mounting a kerb, striking a wall and colliding with a lamp post, a tree and colliding with him.
Mr Young, of Thornwood Avenue, Glasgow, died at the scene.
The trial continues.