He attended Dickinson College in Carlisle, Pennsylvania. He studied law, was admitted to the bar in 1852 and commenced practice in Mauch Chunk, Pennsylvania.
Moving to the Territory of Kansas in 1854, Albright participated in its early development. Though he returned to Pennsylvania and resumed the practice of law in Mauch Chunk in 1856. He was a delegate to the Republican National Conventions in 1860 and 1872.
During the American Civil War, Albright served in the Union Army as major of the 132nd Pennsylvania Infantry.
Honorably mustered out with his regiment and the rank of colonel on May 24, 1863. He was recommissioned as colonel of the Thirty-fourth Pennsylvania Militia during the Gettysburg Campaign on July 3, 1863, and honorably mustered out again on August 10, 1863.
About a year later, on September 4, 1864. He was recommissioned as colonel of the 202nd Pennsylvania Infantry.
On March 7, 1865, President Abraham Lincoln nominated Albright to the honorary grade of brevet brigadier general, United States. Volunteers, to rank from March 7, 1865 and the United States. Senate confirmed the award on March 10, 1865.
Albright was honorably mustered out August 3, 1865. After the war, he resumed the practice of law in Mauch Chunk, Pennsylvania. Albright was elected as a Republican to the Forty-third Congress.
He was not a candidate for reelection in 1874.
He resumed the practice of law and also engaged in manufacturing in Mauch Chunk until his death there in 1880.
Member United States House