Norman Harrison was born in Liverpool, Lancashire, England on 15 September 1873. He was later baptised on St Saviour's Church, Everton on 30 December 1874.
He was the son of an English father, Swainston Harrison (b. 1832 in Shoreditch, London), an accountant, and a Scottish mother, Eliza McIntosh (b. 1843 in Markinch, Fife) who had married in Liverpool in 1866 and who went on to have five children, losing two in infancy. Their children, besides Norman, were: Swainston (b. 1867), Francis Andrew Colpitts (b. 1870), Margaret March (b. 1872) and David March (b. 1878).
Norman first appears on the 1881 census living with his family at 15 Oakfield Road, Everton, Lancashire. The 1891 census shows Norman and his family living at 16 Grant Road, West Derby, Liverpool and he is then described as an apprentice steam engine maker. He served his apprenticeship in the turning, fitting and drawing office of Messrs Higginson & Co., Hurst Street, Liverpool between 1889 to 1894. After completing his apprenticeship he joined the line of Messrs Elder Dempster & Co., as a 4th engineer and later rose to become 3rd and finally 2nd engineer. He left the Elder Dempster Line when, at the age of 23, he gained his Chief Engineer`s certificate of competency and the opportunity to the White Star line as 3rd Engineer aboard the Delphic; he subsequently served on the Athenic (3rd engineer), Corinthic (2nd engineer) and Adriatic (2nd engineer).
Norman was married in Birkenhead, Cheshire in early 1907 to Mary Clare Magee (b. 1877 in Liverpool) but the couple would have no children. They were listed on the 1911 census living at 50 Oakley Road, Southampton but he is also known to have resided at Baden Road, Knotty Ash, Liverpool. Later that year, on 17 November 1911, Norman was elected an Associate Member of the Institution of Mechanical Engineers.
Norman initially joined the Titanic in Belfast, signing-on on 2 April 1912. When he signed-on again in Southampton on 6 April 1912, he gave his local address as 30 Coventry Road, (Southampton). As Junior second engineer he received monthly wages of £18.
Norman Harrison died in the sinking. His body, if recovered, was never identified. His estate, worth £405, 8s, 8d, was administered to his widow on 1 July 1912.
His widow never remarried and died in London on 30 December 1936.