Groom was born at Toowoomba, Queensland, in 1860 to William Henry Groom and his wife Grace (née Littleton). His father, an auctioneer, went on to be a member of both the Queensland Parliament and, being the only transported convict ever to do so, Australian Parliament. After his education at Street Mary"s School, Ipswich, and Brisbane Grammar School, he commenced work at his father"s newspaper, The Toowoomba Chronicle and before long he was promoted to business manager.
As his father"s political interests gained momentum, Henry became the backbone of The Chronicle and in 1900 the business went from being a sole proprietorship to West. H. Groom & Sons with Henry now a director When his father died in August 1901, Henry became managing director and remained in that position until the Grooms sold their interest in the business to the Dunn family in 1922. In 1904, Groom unsuccessfully contested the seat of Drayton and Toowoomba in the Queensland Legislative Assembly following the death of John Fogarty.
In July 1906 however, he was appointed by William Kidston to the Queensland Legislative Council and remained there until the Council was abolished in 1922.
His time in the Council was unremarkable and, except for one major speech on closer settlement, he rarely spoke.
