His greatest achievement was a gold medal at the 1979 Pan American Games. He was also a silver medallist at the Commonwealth Games in 1978 and was a seven-time NCAA champion while at the University of Washington.
He attended the University of Washington and competed for their Washington Huskies collegiate team. While there, he won four straight titles at the NCAA Men's Division I Outdoor Track and Field Championships from 1976 to 1979, including a championship record of 72.36 m (237 ft in). He also won three straight weight throw titles at the NCAA Indoor Championships in the same period. This made him the most successful athlete ever in the NCAA events. He also won four Pacific Coast Conference titles in hammer.
He won four titles at the Canadian Track and Field Championships from 1976 to 1980, including a championship record of 71.76 m (235 ft 5 in) which remains unbeaten. At the 1979 USA Outdoor Track and Field Championships he won the event with a championship record throw of 72.06 m (236 ft 5 in).
His first international medal came at the age of eighteen at the 1975 Pan American Games. He was the first Canadian to win a hammer throw medal at that competition. Three years later at the 1978 Commonwealth Games, held in Edmonton, Alberta, Canada, he became the first Canadian hammer medallist since George Sutherlandin 1934 by taking a silver medal behind Australia's Peter Farmer. The 1979 Pan American Games saw him become his nation's first winner in the event, with a winning throw of 69.64 m (228 ft in). Only shot putter Bruce Pirnie had won a Pan American gold among Canadian throwers.
The last major result of his international career came at the age of twenty three at the Liberty Bell Classic, organised due to the 1980 Summer Olympics boycott that year. He defeated American Boris Djerassi at the alternative event with a mark of 72.62 m (238 ft 3 in) - one of the best of his career. Despite this strong form, he was some way behind the form shown by the Soviets at the 1980 Moscow Olympics, where Yuriy Sedykh set a new world record of 81.80 m (268 ft in). Neilson also competed at the IAAF World Cup event, representing North America, and came fifth in 1977 and fourth in 1981.
|1975||Pan American Games||Mexico City, Mexico||3rd||64.56 m|
|1977||World Cup||Düsseldorf, West Germany||5th||67.18 m|
|1978||Commonwealth Games||Edmonton, Alberta, Canada||2nd||69.92 m|
|1979||Pan American Games||San Juan, Puerto Rico||1st||69.64 m|
|1980||Liberty Bell Classic||Philadelphia, United States||1st||72.62 m|
|1981||World Cup||Rome, Italy||4th||67.56 m|