Henry Shaw was born at 97 Salisbury Street in Toxteth Park, Liverpool, Lancashire, England in the closing months of 1870. He was baptised on 4 May the following year in St Anne's Church in Liverpool.

He was the son of John Thomas Shaw (b. 1831), a coachbuilder by trade, and his wife Mary (b. 1841). His father hailed from Rochdale and his mother from Heywood, both in Lancashire. He had four known siblings: Ann Jane (b. 1868), John (b. 1874), Hugh Lawrence (b. 1877) and Mary (b. 1881).

Henry first appears as a seven-month-old on the 1871 census, still living at 97 Salisbury Street. The family had moved to 12 Hesketh Street in Toxteth Park by the time of the 1881 census and, following that to 227 Falkner Street in Liverpool in time for the 1891 census. Henry by this time was described as a blacksmith's striker. When he went to sea is not certain but he would be absent from home by the time of the 1901 census. His mother, now a widow, was living at 25 Rydal Street, Everton. His father had passed away in 1894 and his mother had taken to becoming a domestic cook to make ends meet.  She is believed to have died prior to 1911 when the next census was taken where she was by now absent; her son Henry would also be absent and likely at sea.

When he signed-on to the Titanic, on 6 April 1912, Henry gave his address as 47 Towcester Street, Liverpool, the home address of his married younger sister Mary Norman and her husband John William, also a seafarer. Henry's last ship had been the Orissa. As a kitchen porter he received monthly wages of £3, 10s.

Henry Shaw died in the sinking. His body, if recovered, was never identified.