Bellany, who died in August last year, produced Self Portrait - Hogmanay in 1968, towards the end of his time at the Royal College of Art.
It is due to be sold on Thursday by the Edinburgh auction house, Lyon & Turnbull. It is valued at between £20,000 to £30,000.
Bellany's works adorned the walls of the Museum of Modern Art, New York, The Metropolitan Museum, New York and Tate Britain, London.
He died surrounded by his family. He had a liver transplant and suffered bouts of illness including a heart attack in a Glasgow street as he walked to an exhibition of his work.
Charlotte Riordan, painting specialist at the auction house said: "John Bellany was one of the best loved Scottish artists of the 20th century. One result of his passing has been the re-emergence of some significant early works on to the market.
"Several new and important motifs can be seen in the painting, the parrot, the skeleton and the element of self portraiture. Bellany always had plastic parrots dotted around his studio. The exaggeration of its beak in this panting is a theme repeated by Bellany with seagulls and puffins in later works."
About this time Bellany visited Germany, with friends the artist Alexander Moffat and poet Alan Bold, where they visited artists on the east side of the Berlin Wall, an experience that was to prove a useful instruction in Social Realism for all three. They took a tour to Buchenwald concentration camp which resulted in a real sense of foreboding and an engagement with human suffering to enter Bellany's work.
Five other Bellanys are in the sale, including The Great Dream, valued at between £6,000-£8,000, a triptych.
Bellany frequently drew inspiration from the East Lothian communities near his birthplace of Port Seton. Many of Bellany's paintings contain the fishing community, either oil paintings of harbours, or portraits of the fishing community people. He later moved to Tuscany.