McCord was born in Montreal to a family of lawyers and businessmen of Irish origin who had emigrated to Canada around the year 1760.
His parents, in an upper class, bilingual marriage, inculcated in McCord a love of art (his father was a connoisseur and his mother was an accomplished watercolour artist) and science from an early age.
Educated at the High School of Montreal, on leaving school he decided to continue the family tradition and study law at McGill University, eventually becoming a magistrate who gained fame by intervening on behalf of the Aboriginal peoples in Canada.
Convinced that an understanding of the past strengthens national identity, he devoted most of his life and personal fortune to gathering and documenting some 15,000 items related to Aboriginal, French and British history in North America.
This man of vision bequeathed his outstanding collection to McGill University, which fulfilled his dream of founding a museum for the benefit of all Canadians.