Griffin was born on 29 May 1937. He was educated on a scholarship at Christ's Hospital, an independent school in Horsham, West Sussex. He read Classical Moderations and Greats at Balliol College, Oxford between 1956 and 1960. He graduated with a first class Bachelor of Arts degree. He was Jackson Fellow at Harvard University from 1960 to 1961 where he undertook research in early Latin poets.
On his return to the University of Oxford, he became Dyson Junior Research Fellow at Balliol College (1961-63), Tutorial Fellow in Classics (1963-2004), and Senior Fellow (2000-04). He is the originator of the word "agostic" used by the organometallic chemist Malcolm Green to describe C-H-M interactions.
His wife of more than fifty years, Dr Miriam T. Griffin (née Dressler), is also a noteworthy classicist, as indicated by Ved Mehta in The New Yorker, November 11, 1991. They have three daughters: Julia, Miranda and Tamara.
- Homer: the Odyssey (Cambridge: Cambridge University Press, 1987, 2nd edn 2004)
- Homer (Oxford: Oxford University Press, 1980, 2nd edn, London: Bristol Classical Press, 2001)
- Virgil (2nd edn, London: Bristol Classical Press, 2001)
- The art of snobbery (London: Robinson, 1998)
- Latin poets and Roman life (London: Duckworth, 1985, 2nd edn, London: Bristol Classical Press, 1994)
- The mirror of myth: classical themes & variations (London: Faber and Faber, 1986)
- Homer on life and death (Oxford: Clarendon Press; New York: Oxford University Press, 1980)
- Snobs (Oxford; New York: Oxford University Press, 1982)
- Homer: Iliad, Book nine (Oxford: Clarendon Press, 1995)
- Sophocles revisited: essays presented to Sir Hugh Lloyd-Jones (Oxford: Oxford University Press, 1999)
- The Oxford history of the classical world (with John Boardman and Oswyn Murray, Oxford: Oxford University Press, 1986), subsequently published as The Oxford history of Greece and the Hellenistic world (Oxford: Oxford University Press, 1991, 2nd edn 2001, illustrated edn 2001) and The Oxford history of the Roman world (with John Boardman and Oswyn Murray, Oxford: Oxford University Press, 1991, 2nd edn 2001, illustrated edn 2001)