New Zealand captain Brendon McCullum scored the fastest ever Test century in a majestic display against Australia on the first day of the second Test.

The 34-year-old needed just 54 balls to reach his 12th century in his 101st and final Test before retiring.

It beat the mark of 56 set by the West Indies' Viv Richards against England in 1986 and equalled by Pakistan's Misbah-ul-Haq against Australia in 2014.

"I was trying to hit every ball for four or six," said McCullum.

"Viv was my idol growing up, he was an incredible cricketer. I'm almost a little bit of embarrassed to go past him, to be honest."

McCullum, whose side lost the opening game of the two-test series and were 32-3 at one point in this one in Christchurch, had a big slice of luck on 39, when he sliced James Pattinson to Mitchell Marsh.

But umpire Richard Kettleborough requested a replay which showed Pattinson had bowled a no-ball.

McCullum went on reach 82 from 48 balls when Josh Hazlewood came in to bowl and, after failing to score from the first two balls of the over, the skipper turned on the power, hitting a six, followed by three fours, to give him the record.