He served as a military stenographer in the Union Army in the Civil War. In 1873 – 1874, he produced a catalog of double stars. He became a fellow of the Royal Astronomical Society. He continued to identify double stars and later published the General Catalogue of 1290 Double Stars. In 1906, he published the Burnham Double Star Catalogue, containing 13,665 pairs of double stars.
For more than fifty years he spent all his free time observing the heavens, principally concerning himself with binary stars. Friedrich Georg Wilhelm von Struve and Otto Wilhelm von Struve had catalogued a good number of binary stars working at the Observatories of Dorpat and Pulkovo and using 23- and 38-cm telescopes. During the 1840s it was believed that essentially all the binary stars visible to the instruments of the day had been discovered. Burnham, with his 15-cm instrument, found 451 new ones from 1872 to 1877. The quality of his work opened the doors of observatories for him and he had access to more powerful instruments at Lick, Yerkes and other observatories. He is credited with having discovered 1340 binary stars.
He received the Gold Medal of the Royal Astronomical Society in 1894.