[4][5] Crosby moved from his home in Renwick, New Zealand to Auckland in the late 1960s and began a motorcycle apprenticeship at a local Kawasaki dealership.
[6][7] The following year, Crosby qualified a Moriwaki Kawasaki on pole position at the 1979 Suzuka 8 Hours, ahead of all the major factory racing teams.
[9][11] In July, Crosby teamed with Wes Cooley on a Yoshimura Suzuki GS1000 motorcycle to win the Suzuka 8 Hours endurance race.
[18] Crosby made a strong impression by winning the pole position at the season opening Austrian Grand Prix held at the fast Salzburgring.
[2] At the Yugoslavian Grand Prix held at the hot Automotodrom Grobnik, Crosby initially battled for the lead but, later admitted that he was out of shape as he faded to a fourth place finish.
[20] Crosby's defense of his TT Formula One title was successful as his Suzuki GS1000 outclassed the Honda RC1000 of his leading rival, Ron Haslam.
Five minutes before his scheduled starting time, Crosby decided to mount a slick tire onto his motorcycle however, the new wheel had the wrong sized sprocket.
[2] The Honda racing team later claimed that they had slowed Haslam and Joey Dunlop's pace upon receiving news of Crosby's time penalty.
Riding at a record setting pace, Crosby won the prestigious Daytona 200 over second place Freddie Spencer.
[22] Crosby jumped into the lead at the start of the season opening Argentine Grand Prix however, he was forced to retire after a couple of laps due to a crankshaft failure.
[22] He qualified on pole position for the Austrian Grand Prix but fell to fourth place in the race when he encountered handling issues with his motorcycle.
A poor start at the beginning of the Nations Grand Prix left Crosby in mid-field however, a spirited ride saw him improve to third place, passing Kenny Roberts before the end of the race.
[22] The rain drenched Dutch TT was stopped after only six laps when Crosby and several other riders crashed on the wet track surface.
[22] After the race was restarted, Crosby made an impressive result by finishing the second leg ahead of Roberts to secure fourth place overall.
[22] When Roberts was forced to withdraw from the championship due to injuries sustained at the British Grand Prix, his V4 Yamaha was given to Crosby for the San Marino Grand Prix however, after he suffered a high speed crash during practice he decided to race on his familiar square-four Yamaha, finishing in third place behind Freddie Spencer and Randy Mamola.
[22] Crosby attempted to ride the V4 Yamaha during practice for the season ending German Grand Prix but, he declared that the experience had taken years off his life.
[22] Despite competing with an older and slower motorcycle, Crosby was able to use his riding skill and determination to finish second overall in the championship behind Franco Uncini.