George Graham was born in Londonderry, Northern Ireland, in 1902. He came to Canada in July 1914 together with his family. He started his soccer with Marshall Wells in 1918. He then played for Hudson Bay, then four seasons with South Side F.C. of Edmonton, Alberta, and three more years with the St. Andrews F.C. of Vancouver.
George came to the United States in January 1926 to play for New Bedford, and then moved on to Philadelphia. He was loaned, together with Dave Turner, to Trenton FC in May 1926 for the remainder of their season.
Dave Turner and George traveled to Toronto in May 1926 to check out the financial situation in soccer in Toronto. They were met at the Union Station in Toronto by representatives of Ulster United who had been tipped off that two star players were coming to Toronto. They both were hired by the T. Eaton Company who were the financial backers of Ulster United.
The blonde centre forward played for the Canadian National Team against the United States in 1926.
He spent the 1927 season with Ulster United in the National Soccer League.
George received many offers to return to the States but turned them all down before going the United States on September 9, 1927 to play for Fall River. Signed for Brooklyn Wanderers in March 1928 but Nat Agar was not happy with his performances and he was put up for sale late in April 1928.
He was the captain of Ulster United in the 1931 season.
Ulster United won the 1934 National Soccer League championship by beating Montreal Carsteel in the finals that were delayed to July 1935.
During the winters of 1934-35 and 1935-36 George played for Kodak Park in the Rochester League.
In 1936 he was said to have scored more than 300 goals since joining Ulster United, and was said to have been angled by many Scottish clubs.
The 168 lbs captain led Ulster United to the 1937 Dominion Cup finals. In the finals they lost to Vancouver Johnston Nationals.
In 1938 he had his twelfth straight season with Ulster United. In an interview with the Edmonton Journal he admitted to be thinking of retiring but not before he had won the Dominion Cup.
Due to the World War Ulster United left the National Soccer before the start of the 1942 season, and instead joined the Toronto & District Senior League.
George helped Ulster United win five trophies in the 1943 season.
He retired from soccer after the 1945 season. When he retired he was said to have scored more than 1,000 goals.
George worked the T. Eaton Company in Toronto for 38 years. The company was famous for employing many of the Ulster United players.
George Graham passed away at the age of 64 on August 7, 1966, in Toronto.