Maxwell was born on 20 February 1812, at 19 Queen Street in Glasgow[1] the eldest son of William Maxwell of Dargavel, Renfrewshire (d.1847), and his wife, Mary Campbell, eldest daughter of John Campbell of Possil, near Glasgow.
He practised his profession until 1845, when he succeeded Sir Charles Gordon of Grimkin as secretary to the Highland Agricultural Society.
The annual shows under his management displayed improvements, and Maxwell paid attention to the collection of agricultural statistics.
In 1848 he was elected a Fellow of the Royal Society of Edinburgh his proposer being Sir John Macneill.
On his own estate at Dargavel, Maxwell carried out costly improvements, especially in the reclamation of waste land.