He attended the common schools and served an apprenticeship at the printer’s trade.
He taught school, studied law, was admitted to the bar in 1817 and commenced practice in Butler, Pennsylvania. He moved to Franklin, Pennsylvania, in 1822 and continued the practice of his profession. Galbraith was elected as a Jacksonian to the Twenty-third and Twenty-fourth Congresses.
He was an unsuccessful candidate for renomination in 1836.
He moved to Erie, Pennsylvania, in 1837, and resumed the practice of law. He was again elected as a Democrat to the Twenty-sixth Congress.
He was not a candidate for renomination in 1840. He again engaged in the practice of law, and was elected president judge of the sixth judicial district in 1851 and served until his death in Erie in 1860.
Interment in Erie Cemetery.
He was a member of the Pennsylvania House of Representatives from 1829 to 1832.