Anna Kirstine Brøndum was born in Skagen, Denmark, the daughter of Erik Andersen Brøndum (1820–1890) and Ane Hedvig Møller (1826–1916). She was the only one of the Skagen Painters who was actually born and grew up in Skagen, where her father owned the Brøndums Hotel. The artistic talent of Anna Ancher became obvious at an early age, and she grew acquainted with pictorial art via the many artists who settled to paint in Skagen, in the north of Jutland.
While she studied drawing for three years at the Vilhelm Kyhn College of Painting in Copenhagen, she developed her own style and was a pioneer in observing the interplay of different colors in natural light. She also studied drawing in Paris at the atelier of Pierre Puvis de Chavannes along with Marie Triepcke, who would marry Peder Severin Krøyer, another Skagen Painter. In 1880 she married fellow Painter Michael Ancher, whom she met in Skagen. They had one child, daughter Helga Ancher. Despite pressure from society that married women should devote themselves to household duties, she continued painting after marriage.
Anna Ancher was considered to be one of the great Danish pictorial artists by virtue of her abilities as a character Painter and colorist. Her art found its expression in Nordic art's modern breakthrough towards a more truthful depiction of reality, e.g. in Blue Ane (1882) and The Girl in the Kitchen (1883–1886).
The Skagen residence of Anne and Michael Ancher was purchased in 1884. In 1913, a large studio annex was added to the property, and this also formed part of what is on display today. Upon her death in 1964, the Anchers' daughter, Helga, left the house and all of its contents to a foundation. The former residence was restored and opened as a museum and visitor attraction.
Ancher preferred to paint interiors and simple themes from the everyday lives of the Skagen people, especially fishermen, women and children. She was intensely preoccupied with exploring light and color, as in Interior with Clematis (1913). She also created more complex compositions such as A Funeral (1891). Anna Ancher's works often represented Danish art abroad. She was awarded the Ingenio et Arti medal in 1913 and the Tagea Brandt Rejselegat in 1924.
In 1967, Michael and Anna Ancher's house (Anchers Hus) in Skagen was converted into a museum by the Helga Ancher Foundation before Anchers Hus opened to the public for tours. Original furniture and paintings created by the Anchers and other Skagen artists are shown in the restored home and studio. Art exhibitions are arranged in the Saxild House (Saxilds Gaard), another building on the property, and is filled with displays of paintings by Michael and Anna Ancher as well as many other Skagen Painters who made up their circle of friends.
Anna and Michael Ancher were featured on the front side of the DKK1000 bill, which came into circulation on 25 November 2004 and was subsequently replaced. The front of the banknote had a double portrait of Anna and Michael Ancher, derived from two 1884 paintings by Peder Severin Krøyer, which originally hung on the walls in the dining room at Brøndums Hotel.