Molloy was born in Galway and was educated at Coláiste Iognáid and University College Galway. Molloy was first elected to Dáil Éireann as a Fianna Fáil Teachta Dála (TD) for the Galway West constituency at the 1965 general election.
In 1968, he was also elected Mayor of Galway. The following year he was appointed to the Cabinet as Parliamentary Secretary to the Minister for Education. From 1970 to 1973 he served as Minister for Local Government. When Fianna Fáil returned to power in 1977 he became Minister for Defence in the final government of Jack Lynch.
In 1979, Molloy supported George Colley in the Fianna Fáil leadership contest. However Charles Haughey was the eventual victor. After this Molloy was dropped from the Cabinet, becoming a member of the Gang of 22 who opposed Haughey's leadership of the party. In 1986 Molloy resigned from Fianna Fáil and joined the newly formed Progressive Democrats.
In 1989, the party entered into coalition with Fianna Fáil, with Molloy becoming Minister for Energy. That same year he contested the European Parliament Elections but was unsuccessful in his attempt. He stood at the European Parliament elections again in 1994 but was again unsuccessful. Following the 1997 general election, Molloy helped in the negotiations for forming the coalition government between the Progressive Democrats and Fianna Fáil. On that occasion, he became Minister of State at the Department of the Environment.
Molloy retired from politics just before the 2002 general election amid controversy regarding constituency letters intervening in the rape case of Barbara Naughton.