He was born in York in 1841, the youngest of the fourteen children of the artist William Moore of York who in the first half of the 19th century enjoyed a considerable reputation in the North of England as a painter of portraits and landscape.
In his childhood Albert Moore showed an extraordinary love of art, and as he was encouraged in his tastes by his father and brothers, two of whom afterwards became famous as artists — John Collingham Moore and Henry Moore, and he was able to begin the active exercise of his profession at an unusually early age.
His first exhibited works were two drawings which he sent to the Royal Academy in 1857. A year later he became a student in the Royal Academy schools; but after working in them for a few months only he decided that he would be more profitably occupied in independent practice. During the period that extended from 1858 to 1870, though he produced and exhibited many pictures and drawings, he gave up much of his time to decorative work of various kinds, and painted, in 1863, a series of wall decorations at Coombe Abbey, the seat of the Earl of Craven; in 1865 and 1866 some elaborate compositions:The Last Supper and The Feeding of the Five Thousand on the chancel walls of the church of St. Alban's, Rochdale; and in 1868 A Greek Play, an important panel in tempera for the proscenium of the Queen's Theatre in Long Acre