Griffith was educated at the Trinity College, Dublin (M.A., 1832) and called to the Irish bar.
[1] On 31 October 1851[3] Griffith was sworn in as a nominated member of the Victorian Legislative Council, a position he held until resigning June 1852.
[3] Griffith was then elected to the council as a member for Normanby, Dundas and Follett, on 1 June 1853,[4] he resigned in April 1854, but was re-elected in June 1854 and held the seat until the unicameral Council was abolished in March 1856.
[1] Griffith was elected to the inaugural Victorian Legislative Assembly for Dundas and Follett, being sworn in in November 1856.
Griffith died childless on 31 July 1863 at his home in Dandenong Road, South Yarra, Victoria, Australia.