The following lists events that happened during 1788 in Australia.
- Monarch - George III
- Governor of New South Wales – Captain Arthur Phillip
- Governor of Norfolk Island – Philip Gidley King
- Commanding officer of the colony's marine presence – Major Robert Ross
- 18 January – HMS Supply of the First Fleet arrives in Botany Bay.
- 26 January – The First Fleet lands in Port Jackson, Australia from Portsmouth, England, and establishes the English penal colony of New South Wales – the first European settlement in Australia.
- 6 February – The first female convicts arrive at Port Jackson.
- 9 February – The colony of New South Wales is formally proclaimed. Phillip is sworn in as Captain-General and Governor-in-Chief.
- 18 February – Lord Howe Island is discovered by Henry Lidgbird Ball on HMS Supply.
- 27 February – A convict, Thomas Barrett, receives the first death sentence in the colony.
- 6 March – Philip Gidley King is sent from the Port Jackson colony to settle Norfolk Island with a party of fifteen convicts and seven men.
- 15 April – Phillip King explores northwards to Manly, and sights the Blue Mountains.
- 23 April – Governor Phillip explores the area now known as Parramatta, west of Sydney.
- 29 May – Two convicts are killed by Aboriginals at Rushcutters Bay; Phillip leads a punitive attack on the Aborigines on 31 May.
- 5 June – All the settlement's cattle brought from Cape Town escape; they are not recaptured until November 1795.
- 21 July – First sitting of the Court of Civil Jurisdiction.
- September – Sydney's first road, from the Governor's House to Dawes Point, is completed.
- October – Due to poor conditions, scurvy breaks out. Phillip orders strict rationing and sends HMS Sirius to Cape Town for supplies.
- 2 November – A second settlement is established at Rose Hill, which will later become Parramatta.
- 4 January – Johann Menge, South Australian explorer and geologist (d. 1852)
- 16 January – Hannibal Hawkins Macarthur, New South Wales politician and businessman (d. 1861)
- 17 April – Charles Hervey Bagot, South Australian pastoralist, mine owner and parliamentarian (d. 1880)
- 22 May – William Broughton, bishop (d. 1853)
- 2 August – Charles Hardwicke, Tasmanian explorer (d. 1880)
- 24 August – Osmond Gilles, South Australian colonial treasurer (d. 1866)
- 24 October – John Burdett Wittenoom, Swan River Colony clergyman (d. 1855)
- date unknown
- Charles Fraser, botanist (d. 1831)
- Frederick Goulburn, first Colonial Secretary of New South Wales (d. 1837)
- Frederick Irwin, acting Governor of Western Australia (d. 1860)
- John Ovens, explorer (d. 1825)
- Thomas Pamphlett, convict and castaway (d. 1838)
- Henry Willey Reveley, Swan River Colony civil engineer (d. 1875)
- Edward Buckley Wynyard, New South Wales politician (d. 1864)
- 5 June – Ruth Bowyer, convict (b. c. 1761)
- The World Upside Down – Australia 1788–1930, National Library of Australia.
- Anderson, Atholl (2003). "Investigating early settlement on Lord Howe Island". Australian Archaeology.
- Cable, K. J. "Broughton, William Grant (1788–1853)". Australian Dictionary of Biography. National Centre of Biography, Australian National University. Retrieved 26 June 2018.
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