Graham was born in Annaberg-Buchholz, Bezirk Karl-Marx-Stadt. Under her maiden name of Yvonne Grabner, she first came to prominence in 1983 competing for East Germany, winning a bronze medal at the 1983 European Junior Championships. Later, she married fellow East German athlete, Volker Mai. While competing as Yvonne Mai, she won a bronze medal at the 1989 World Indoor Championships. She competed for East Germany until 1990 and then a United Germany. In 1993 she married Jamaican 400 m hurdler Winthrop Graham and obtained Jamaican citizenship. She holds the Jamaican national records for 1500 metres, mile, and 3000 metres.