The tree was purchased at Woolworths in Dundee in 1937 and has only recently been unearthed from a loft where it was kept for 24 years.
Standing just 27in (69cm) high, it was bought by a family to celebrate the arrival of baby James Smith, who was born that year.
Mr Smith's daughter, Claire Barnett, a teacher from Fife, said: "My gran, Catherine Smith, bought it for my dad's first Christmas in 1937, not long before the start of the Second World War in 1939.
"After that, it became the main tree in my grandmother's home in Dundee for decades. She decorated it every Christmas until she died in 1995 at the age of 89."
The tree is set to go under the hammer at Hansons Auctioneers in Etwall, Derbyshire, on Thursday December 19, with an estimated price of £100-£150.
But it could exceed that amount following a similar Hansons auction in 2017 when the American Christmas Tree Association bought one for £420.
Ms Barnett said Christmas has changed a lot since her father, now 83, was born.
"On Christmas Day he remembers getting an orange, a shiny penny, a game and some sweets in his sock by the fire," she said.
"There were some candles on the tree, which has small candle holders on the end of some of the branches as well as some red berries.
"Christmas dinner would be a chicken, which was a luxury back then, and he would have Christmas dinner with his mother and aunt."
The tree was found in the family loft during a clear-out and, despite not being used since 1995, is still intact.
Charles Hanson, owner of Hansons Auctioneers, said: "This is a wonderful reminder of Christmas without excess in the late 1930s and during the Second World War. This humble tree, bought for a modest amount, was treasured by one family and came out every Christmas for 58 years.
"It's in remarkable condition considering its age and deserves to be on show and admired.
"It was bought at Woolworths, a department store millions of British people knew and loved. Woollies is no longer on our high streets but in its heyday it played a huge part in Christmas shopping."
He added: "Life today is very different. Shops, both online and in our towns and cities, are awash with festive merchandise. Families splash out hundreds, if not thousands, on Christmas every year ... finds like this modest tree remind us that you don't need to spend a fortune to enjoy a happy Christmas."
Department store Woolworths started selling some of the first mass-produced artificial trees in the 1920s.
But the first artificial Christmas trees were developed in Germany during the 19th century and were made using goose feathers dyed green.