Grierson was born in Glenageary, County Dublin. His father and grandfather (George Grierson) were well-known Dublin printers and publishers. His mother Isabella was the daughter of Henry Ruxton of Ardee. He was educated at St. Bees School, then from the age of 13 at Shrewsbury. He then went up to Trinity College, Dublin, where he was a student of mathematics. Grierson qualified for the Indian Civil Service in 1871 ranking twenty-eighth for the year. He continued studies at Trinity College for two probationary years where he was influenced by Robert Atkinson, professor of oriental languages. He took a deep interest in languages, won prizes for studies in Sanskrit and Hindustani before leaving for the Bengal Presidency in 1873. First posted to Bankipore in Bihar, he became Magistrate and Collector at Patna and still later in 1896, Opium Agent for Bihar. He married Lucy Elizabeth Jean, daughter of Maurice Henry Fitzgerald Collis, a Dublin surgeon, in 1880 but they had no children.