Maxwell Balfour was the second son of a Scottish engineer. In 1884 he entered Clifton College. In 1892 he entered New College, Oxford and enrolled in drawing classes at the Slade School. Balfour spent the winter of 1892 touring Italy with Charles Aitken, curator of the Tate Gallery, and returned to England determined to become a painter. In 1897 he became a full time student at the Slade and took lodgings at 118 Cheyne Walk (once the residence of Turner). That same year, he traveled to Venice and later India to visit his brother in Cawnpore. While in India he also made stops at Kashmir and Bombay. Balfour returned to the Slade in 1897 and was commissioned by the National Trust to make a series of lithographs, now in the British Museum.
On the occasion of Queen Victoria's Diamond Jubilee in 1897, Balfour made drawings of the procession, with the intention of painting several large pictures of the event; however, his time was increasingly taken up with portrait commissions and the project was never completed. Ill health forced Balfour to cease painting and in 1909 he moved to France. At the outbreak of World War I he moved back to England where he died a few weeks later.