Jeff played his youth hockey in the fertile hockey environment of Minnesota. On his way up, he appeared to be a solid professional prospect as early as his days in high school. He was drafted 111th overall by the Buffalo Sabres in 1982 Entry Draft. At age 18, however, he elected to attend university first before contemplating a career with the pros.
From 1983 to 1986, the right winger studied by day and skated for the Michigan State Spartans of the CCHA at night. In his final season, he became a solid scorer and was selected to the NCAA Championship All-Tournament Team.
In 1986-87, Parker turned pro with the Buffalo Sabres. His role at the NHL level, however, was much more defensive in orientation than during his college days. Throughout the five seasons that followed, he struggled to win ice time with the Sabres on a consistent basis. Each year, he spent at least part of his season with the Rochester Americans of the American Hockey League. It wasn't until 1989-90 that he earned his one and only complete campaign in the NHL. During that time, he struggled offensively as a fourth-line winger with a limited mandate to fill in gaps wherever needed.
In 1990, Parker was traded to the Winnipeg Jets as part of the big Phil Housley for Dale Hawerchuk swap. However shortly thereafter the once bright career of Jeff Parker became murky. Parker quit hockey without ever having played with the Jets. He didn't return until February 5, 1991, when he exercised his new status as an unrestricted free agent to sign with the Pittsburgh Penguins.
The Penguins asked Jeff to report to their farm in Muskegon in order to get him back into game condition, but after only 11 games with the IHL Lumberjacks Parker was traded to the Hartford Whalers. It was the second significant trade Parker was involved with, this time the famous Ron Francis and Ulf Sameulsson trade that helped Pittsburgh win the next two Stanley Cups.
Parker made his brief return to the National Hockey League while with the Whalers. He was immediately called up but only participated in 4 regular season contests and collected no points.
Jeff decided to pursue non-hockey interests at the conclusion that season. He retired with 141 games played, 16 goals, 19 assists and 35 career points.