Robert Graham was born in the parish of Barony, Glasgow, Lanarkshire, Scotland, on 15 May 1820. He was the fifth child and third son of Barbara Stirling Rennie and her husband, Robert Graham, a farmer and coal merchant.
On 18 June 1842 Robert Graham left for Auckland, New Zealand, on the Jane Gifford. He and his brother David went into partnership as general merchants in Kororareka (Russell) and Auckland, where their premises were on the corner of Queen Street and Shortland Crescent.
At Waiwera in 1845 Robert Graham purchased 20 acres of land on the foreshore, including hot springs, whose tourist potential he had recognised. He built a hotel and later increased his landholdings. In 1848 he bought over 500 acres at Ellerslie.
In March 1849 Graham left for California, where he spent the next three years. His partnership with his brother was dissolved in 1850. On 11 June of that year, in San Francisco, Robert married Sophia Swann. They were to have two daughters and a son before Sophia's death in 1862. On his return to Auckland Graham erected Ellerslie House, laid out gardens, and built a zoo. In 1857 he established a pedigree cattle and sheep farm on Motutapu, which he farmed until 1869. His other landholdings included Motuihe, which he farmed with his brother John, and Lamb Hill, a 2,500 acre farm near Waiuku. In 1881 he sold 101 acres of the Ellerslie property to the Auckland Racing Club.
Graham was MHR for the Southern Division of Auckland from 1855 to 1860, and for Franklin from 1861 to 1868. He vigorously promoted Auckland's interests and opposed the removal of the seat of government to Wellington in 1865. In the Auckland Provincial Council Graham represented the Southern Division from 1855 to 1857 and Franklin from 1865 to 1869. He was elected superintendent in 1862, and held the post until September 1865. During his tenure the council engaged in a vigorous programme of public works and building.
In 1862 Graham had been twice shipwrecked. En route to Wellington the White Swan foundered off the Wairarapa coast on 29 June, and on his return voyage to Auckland the Lord Worsley was wrecked off the south Taranaki coast on 1 September. Graham took a leading part in negotiations with local Maori for safe conduct for the survivors.
After the opening of the Thames goldfield in 1867 Graham acquired land at Kauaeranga in 1868, subdivided it and laid out a settlement, which became known as Grahamstown, part of the present township of Thames. At Tararu, north of the town, Graham laid out public gardens and a racetrack, and built a hotel. On 2 June 1870 at Auckland he married Jane Stephenson Horne. They had three sons.
Fluent in Maori, Graham travelled to Maketu in June 1878 and mediated in the conflict between Te Pokiha Taranui and Petera Te Pukuatua of Te Arawa. In return for his assistance he was offered land at Te Koutu by Rotorua Maori and at Wairakei by Taupo Maori. In January 1879 Graham occupied the land at Te Koutu. However, in May he was prosecuted for unlawful possession. After litigation and a petition to Parliament he was eventually permitted to purchase 10 acres within Te Koutu block.
At Wairakei, aware of the tourist potential of the area, Graham managed to secure 4,200 acres, including the geysers and the Huka Falls, despite the passing of the Thermal Springs Districts Act 1881 to prevent such transfers. His actions at Ohinemutu were even more controversial. From December 1879 until 1882 he was involved in a complex intrigue to obtain control of the Ohinemutu (later Lake House) Hotel. Graham also operated the Terrace Hotel at Te Wairoa, which was destroyed in the eruption of Mt Tarawera in 1886.
Graham advertised his tourist resorts with a publication about Waiwera (about 1876) and Graham's guide to the hot lakes (1884). He died in Auckland on 26 May 1885. Jane Graham and her sons continued to operate the hotels at Ohinemutu and Wairakei for many years.