He married actor Nell Feeney in 1994, with whom he had twins Thomas and Grace (born March 20, 1995).

Shane Connor graduated from the Victorian College of the Arts in the early 1980s. He worked steadily in film, theatre and television for many years.

His television credits include the Channel Seven series Fire, the Australian Broadcasting Corporation drama Heartland and the miniseries The Harp in the South and Poor Man's Orange. Awards include the 1984 Penguin Award for best actor, 1995 Green Room Award for outstanding fringe performer and a nomination for the 1998 AFI Award for best actor in a leading role in a television drama.

Connor also played guest roles in Australian soap operas. He played the recurring role of Bongo Connors in the women's prison drama serial Prisoner in 1986. Earlier he had a brief guest role in the series as Kevin, husband of Cheryll (Lisa Aldenhoven). Connor had a brief role as another biker, Angel, in Sons and Daughters in 1986.

Connor later played the key on-going role of builder Joe Scully in Neighbours starting in 1999. Eight years previously (in 1991) he had played a one-off character called Phil Hoffman in episode #1.1410.

Connor was fired from the series after four years in the role. He sued the show's producer, Grundy Television, for wrongful termination of his contract, seeking about $200,000.

The court hearing heard that he had an amphetamine drug habit while performing on the show. Connor's older brother died in June 2001 and he had been badly affected by this, leading to the drug habit. Members of the cast and crew had complained about his behaviour at work. This included alleged aggressive bahaviour and lateness that delayed production. After being confronted about his problem he met with the cast in May 2003 and admitted the problem and apologised.

He was sacked from the series in September 2003, several months after receiving a written warning from producers and overcoming his amphetamine habit. There had been ongoing hostility between him and Janet Andrewartha who played his wife Lyn; she had been the source of the vast majority of complaints about him.

Connor won the case and was awarded over $230,000.

In the show's storyline his character Joe Scully was said to have left to work on a relative's farm. These were said to be temporary plans, but Joe never returned. His wife Lyn (Janet Andrewartha) remained in the series and later their marriage was said to have been dissolved. Lyn subsequently had a relationship with another Joe, the returning Joe Mangel (Mark Little).