In 1874, the playwright Henrik Ibsen asked Grieg if he would write some music to accompany his new play Peer Gynt, in which the hero travels around the world, having many strange adventures in distant lands. At that time Grieg had developed a reputation as a composer of Nordic music and his talents seemed to make him the ideal musician to complement Ibsen's poetic evocation of the Norwegian character. Grieg was initially reluctant to take on the task, but the chance to write pieces describing exotic locations and unusual scenes captured his imagination. At first, however work progressed slowly, and he described it to friends as "an unmanageable project". However, in time he warmed to the task. His wife wrote that "The more he saturated his mind with the powerful poem, the more clearly he saw that he was the right man for a work of such witchery and so permeated with the Norwegian spirit". He still had to overcome practical difficulties because the theatre producers specified the exact duration of each musical number. Grieg complained that he could not compose as he wanted and about the necessary brevity of the pieces.

However, despite all difficulties he completed 90 mins of orchestral music in 26 movements. The production must have lasted for around 3 hours, and was an acclaimed success. The music was not heard outside the theatre for some time, and was not published until 1908. However, Grieg made two suites each containing four movements. The first was published in 1888, and the second in 1891. Both suites have become very popular concert items and are among the most famous orchestral works that he wrote.

The first suite contains four movements: the first expresses feelings of joy at waking in the morning; the second is a touching lament played on muted strings; the third, again played on muted strings, is an exotic mazurka, and the final movement, certainly the best known piece he wrote, is the wild and bloodthirsty dance in the hall of the Mountain King. Grieg wrote of it "For the Hall of the Mountain King I have written something that so reeks of cowpats, ultra-Norwegianism, and 'to-thyself-be-enough-ness' that I can't bear to hear it, though I hope that the irony will make itself felt." Avoiding commitment and just doing enough to get by was central to Ibsen's satirical portrayal of the Norwegian character.

Grieg's first Peer Gynt suite was performed by the Portobello orchestra on the 7th December 2019, conducted by Sam Jones.