One of the most important paintings to come to Australia, Whistler's Mother, a "complex and fascinating" story about a painter and his relationship with his mother, goes on display at the National Gallery of Victoria (NGV) this week.

The 1.6-metre-tall painting, officially called Portrait of the artist's mother, was painted in 1871 and is one of the most recognisable paintings in the world.

It depicts painter James McNeill Whistler's mother, Anna Whistler.

"He was quite a character, and when his mother came to stay [after] she was widowed he said that he would have to purify his house," said Dr Isobel Crombie, assistant director of the NGV, about the austere painting.

"He would have to move out his mistress and he had to move out the serving girl who had just had his child.

"They were two very different personalities."

Anna Whistler was a devout Episcopalian who tried to exert a "virtuous power" over her son's life but failed.

"The one area they did correspond was in their attitude to work," Dr Crombie said.

"Whistler was an extremely dedicated artist and I like to think of this painting in some ways as being his mother's revenge.

"It was the first time I think that he listened to her and it's been the most successful painting for him."

Dr Crombie believes the painting is popular because it is a "distillation on the meanings of motherhood."

"If you look at the way that he's painted her beautiful old skin and her hands, you can see that it's not that he hated his mother by any means," she said.

"He really did adore his mother in many ways."

James McNeill Whistler said he would have to "purify his home" before his widowed mother came to live with him. ( Supplied: National Gallery of Victoria )

In category of Mona Lisa, The Scream

The exhibition looks at Whistler's career as an artist, his mother and some of the other painters, including Australian John Longstaff, who were influenced by his work.

"It actually forms a rich and complex story, I think, then in the final room we just have the painting for people to enjoy, and hopefully see afresh," Dr Crombie said.

Whistler's Mother is in the same category as Mona Lisa or Munch's The Scream, and difficult to put a value on, she said.

"A painting like this, which is probably one of the most important paintings to come to Australia, in some sense, they go beyond that kind of monetary value because they're irreplaceable," Dr Crombie said.

"It's definitely one of them.

"If you think in the history of art there's probably only a handful of paintings that you would call icons which everybody knows, and I can't think of another example of a more important painting that has come to Australia."