Suh was born in Taegu, South Korea. Due to a heart defect, he left school in his teens and studied art under Paris-trained teachers. He moved to the United States to continue his education at Hastings College in Nebraska, and while a student there, discovered that he required heart surgery. A Jehovah’s Witness, Suh could not accept blood transfusions, and his case became known to heart surgeon Denton Cooley, who agreed to perform the surgery free of charge. In thanks, Suh painted Cooley’s portrait; as a result, he began to receive commissions to paint others. Suh was approached in 1987 by Dr. Gregg Plock, an old friend from Hastings College and a Hopkins medical student preparing for graduation at the time, to paint a portrait of Henry Seidel. Seidel's portrait commission led to the portrait commissions of John Littlefield and William Zinkham. Suh continued his studies at The Art Students League of New York and the National Academy of Design, also in New York.
Suh maintained his studio in Carnegie Hall and became a member of the Society of Illustrators. The Republican National Committee in 1984 selected Suh to paint a portrait of President Ronald Reagan. One year later, he executed a double portrait of President Reagan and Russian President Mikhail Gorbachev. From 1990-1995 he taught at the Colorado Institute of Art (now The Art Institute of Colorado). Suh returned to South Korea in 2008.