It is a "viola quintet" in that it is scored for string quartet with a second viola. Brahms composed the work in three movements:
Allegro non troppo ma con brio: in sonata form. The first subject group is in F major, while the second is in A major, the first of the "pervasive mediant relationships" in this work.
Grave ed appassionato – Allegretto vivace – Tempo I – Presto – Tempo I: in double variation form. The first theme is based on a sarabande Brahms wrote in 1854, while the second theme is based on a gavotte that he wrote in the same year. The movement starts in C-sharp major, and ends in A major, another mediant relationship.
Allegro energico – Presto: in a fusion of sonata and contrapuntal forms. The final key of the previous movement, A major, and the key of this movement, F major, represent another mediant relationship.
Brahms described the quintet to his friend Clara Schumann as "one of [his] finest works" and told Simrock, "You have never before had such a beautiful work from me."