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.