The son of Marguerite McLeod and Samuel Le Roy Barber, he was born into a comfortable, educated, social, and distinguished American family. His father was a physician; his mother, called Daisy, was a pianist of English-Scottish-Irish descent whose family had lived in the United States since the time of the Revolutionary War. His aunt, Louise Homer, was a leading contralto at the Metropolitan Opera; his uncle, Sidney Homer, was a composer of American art songs. Louise Homer is known to have influenced Barber's interest in voice. Through his aunt, Barber had access to many great singers and songs.

At a very early age, Barber became profoundly interested in music, and it was apparent that he had great musical talent and ability. He began studying the piano at the age of 6 and at age 7 composed his first work, Sadness, a 23-measure solo piano piece in C minor.  

When he was 14, he entered the Curtis Institute of Music in Philadelphia, where he studied piano with Isabelle Vengerova, composition with Rosario Scalero, and voice with Emilio de Gogorza. He began composing seriously in his late teenage years. Around the same time, he met fellow Curtis schoolmate Gian Carlo Menotti, who became his partner in life as well as in their shared profession. At the Curtis Institute, Barber was a triple prodigy in composition, voice, and piano. He soon became a favorite of the conservatory's founder, Mary Louise Curtis Bok. It was through Mrs. Bok that Barber was introduced to his lifelong publisher, the Schirmer family. At the age of 18, Barber won the Joseph H. Bearns Prize from Columbia University for his violin sonata (now lost or destroyed by the composer).

From his early to late twenties, Barber wrote a flurry of successful compositions, launching him into the spotlight of the classical music world. His first orchestral work, an overture to The School for Scandal, was composed in 1931 when he was 21 years old. It premiered successfully two years later in a performance given by the Philadelphia Orchestra under conductor Alexander Smallens. In 1935, at the age of 25, he was awarded the American Prix de Rome and was the recipient of a Pulitzer traveling scholarship which allowed him to study abroad in 1935–1936. He was later awarded a Guggenheim Fellowship in 1946.

When Barber was 28, his Adagio for Strings was performed by the NBC Symphony Orchestra under the direction of Arturo Toscanini in 1938, along with his first Essay for Orchestra. The Adagio had been arranged from the slow movement of Barber's String Quartet, Op. 11. 

In 1942, Barber joined the Army Air Corps; there, he was commissioned to write his Second Symphony, a work he later suppressed. Composed in 1943, the symphony was originally titled Symphony Dedicated to the Air Forces and was premiered in early 1944 by Serge Koussevitsky and the Boston Symphony Orchestra. Barber revised the symphony in 1947; it was published by G. Schirmer, and recorded the following year by the New Symphony Orchestra of London conducted by the composer, but in 1964 Barber destroyed the score. 

Barber won the Pulitzer Prize twice: in 1958 for his first opera Vanessa, and in 1963 for his Concerto for Piano and Orchestra.

Barber spent many years in isolation after the harsh rejection of his third opera Antony and Cleopatra. He suffered from depression, and was also beset by alcoholism. The opera was written for and premiered at the opening of the new Metropolitan Opera House on September 16, 1966. After this setback, Barber continued to write music until he was almost 70 years old. The Third Essay for orchestra (1978) was his last major work.