At the age of 17, he won the West Wales snooker championship. He compiled his first century break when he was 24, the same year that he first entered the Welsh Amateur Championship, finishing as runner up. He played in the amateur home internationals fourteen times, winning twelve of his matches, and after winning the Welsh Amateur Championship in 1975, gained a place at the 1976 World Amateur Snooker Championship where he reached the quarter-finals. Griffiths won the English Amateur Championship in 1977 and 1978 before turning professional on 1 June 1978, having been accepted as a member by the World Professional Billiards and Snooker Association at its meeting during the 1978 World Snooker Championship. Anticipating his acceptance as a professional, "Snooker Scene" wrote in May 1978 that "his power screws and long potting are second to no one's ... it will not be in the least surprising, if very soon he becomes a serious challenger for Snooker's top professional titles."