The names of the Scottish Colourists – Peploe, Fergusson, Hunter and Cadell – are so familiar we tend to think we know their paintings by heart.

But of the four, George Leslie Hunter is the least known, and has not received the same level of attention and acclaim as the other three. A new retrospective, the first for 70 years, aims to address that anomaly. The exhibition is part of the Edinburgh Art Festival and is accompanied by a book, Hunter Revisited, the first major biography of the artist for 75 years, by Bill Smith and Jill Marriner.

What strikes you immediately on viewing these 80 works, sourced from private and public collections across the UK and displayed over two floors, is the breathtaking range of styles and media, as well as colour, that Hunter experimented with during his short, restless and highly productive life: he died in 1931 aged 54, having spent prolonged and repeated periods in the US, Paris, Pas-de-Calais, Provence, Holland, Venice, Florence and London as well as his native Scotland.

He never received formal training as an artist and he was heavily influenced by a number of artists such as Vermeer, Hals, Velasquez, Vuillard, Matisse and the Post-Impressionists Van Gogh and Cezanne.

There are some lovely reminders of his skill in his lively ink-and-crayon and ink-and-wash works, such as Plage and Cafe Scenes in Juan Les Pins, while his stunning and familiar still lives in bright oils on black backgrounds – such as the iconic Peonies In A Chinese Vase (c1925) show his developing fascination with Matisse and the Dutch movement. The vibrant greens and reds of Pathway, Loch Lomond is one of his iconic Scottish paintings. Yet for me his rare, impressionistic watercolour, Interior Of A French Church (1922), is a highlight of this impressive and revealing collection.

Also to look out for are some fascinating examples from Hunter's early career as an illustrator for newspapers and magazines while living in San Francisco from 1899, which earned him money while he worked on his painting. These, and small figurative drawings in pencil and crayon and wash and chalk on grey paper, are precious relics of his time in San Francisco as a young man just starting out: after two years away, sketching and painting in Paris, Holland and London, and with enough to put together his first solo show, he returned in 1906 to find that a fire sparked by an earthquake had destroyed all his other work. As a result the solo exhibition was postponed.

Born in Rothesay on the island of Bute, Hunter moved with his family to California following the death of two siblings in their early 20s within a month of each other. He chose to stay in the US when his family later returned to Scotland, and dropped the forename George in favour of Leslie, but after the disaster he joined them in Glasgow, frequently visiting Paris.

His first solo exhibition, comprising mainly still-life paintings, took place at Alexander Reid's gallery in Glasgow in 1913. It was a huge success and was followed by a second there in 1916 and a further two in 1923 and 1925. Hunter continued painting at Etaples in the Pas-de-Calais, producing beach and harbour scenes that show a lightening of the palette and an attempt at working with a broader and more loaded brush. Although he was enthralled by van Gogh, it was Cezanne who influenced him most at this time. When he returned to France in 1925 he resumed his interest in still-life and the rich colours of Matisse.

Landscape paintings from his time in Fife and Italy from 1919 show this influence in a distinctive application of colour and creation of form. The warm, gentle series of oils from Ceres, Crail and Lower Largo are as beguiling as his Reflections, Balloch.

Hunter's reputation was enhanced when his work was shown with that of Peploe and Cadell in London in 1923. The next year, Peploe, Fergusson, Hunter and Cadell exhibited together for the first time in Paris under the banner Les Peintres De l'Ecosse Moderne. Hunter was commended by art critics in his lifetime and his paintings remain popular, with one making more than £430,000 at auction in 2009.

Lynne Halfpenny, head of culture and sport at Edinburgh City Council, says: "There is a real appetite among Scots and visitors alike for the work of Scottish artists. Hunter's work is distinctive and colourful but there has been little opportunity to see so much of it under one roof until now."

Upstairs, a complementary exhibition, The Scottish Colourists: Inspiration And Influence, includes works by some of the artists who influenced Hunter, and those who have been influenced by him.

Leslie Hunter: A Life In Colour runs until October 14 (£5; £3.50) at the City Art Centre., 2 Market Street, Edinburgh. 0131 529 3993, www.edinburghmuseums.org.uk