He studied literature and medicine at the University of Pennsylvania, and after graduating in 1883, he worked as a staff physician at the Pennsylvania Hospital, until he moved to Wyoming.
He was the second Governor of Wyoming after that state joined the Union in 1890. In 1885, Barber moved to Wyoming to take up a position as surgeon in charge of the military hospital at Fort Fetterman. He was promoted to Acting Surgeon in the United States Army and accompanied General George Crook"s expedition to Arizona, then was assigned to duty at Fort Doctorate. A. Russell.
After resigning from the United States military, he was in charge of the hospital of the Wyoming Stock Association.
In 1889, he began private practice in Cheyenne. In 1890, Barber was elected Secretary of State of Wyoming as a Republican.
Just eleven months later, however, Governor Francis East. Warren resigned to take up a United States Senate seat, and Barber was catapulted to the position of Acting Governor on November 24, 1890. During his administration, he called out state troops to quell a Pine Ridge Indian outbreak and asked for federal assistance with the Rustler War (The War on Powder River) between cattlemen (WSGA) and cowboys (small time ranchers) in Johnson County in 1892.
When John East. Osborne was elected on January 2, 1893, Barber continued on as Secretary of State under Osborne until his term ran out in 1895 and then returned to Cheyenne and his practice.
Barber rejoined the military in 1898, acting as assistant surgeon for the Spanish American War. He then returned to his practice of medicine in Cheyenne. Barber is interred at Lakeview Cemetery, in Cheyenne, Laramie County, Wyoming.