The work is among Grieg's earliest important works, written by the 24-year-old composer in 1868 in Søllerød, Denmark, during one of his visits there to benefit from the climate, which was warmer than that of his native Norway.
Grieg's concerto is often compared to the Piano Concerto of Robert Schumann — it is in the same key, the opening descending flourish on the piano is similar, and the overall style is considered to be closer to Schumann than any other single composer. Incidentally, both wrote only one concerto for piano. Grieg had heard Schumann's concerto played by Clara Schumann in Leipzig in 1858 (1859 is given by alternative sources), and was greatly influenced by Schumann's style generally, having been taught the piano by Schumann's friend, Ernst Ferdinand Wenzel. Compact disc recordings often pair the two concertos.
Additionally, Grieg's work provides evidence of his interest in Norwegian folk music; the opening flourish is based around the motif of a falling minor second (see interval) followed by a falling major third, which is typical of the folk music of Grieg's native country. This specific motif occurs in other works by Grieg, including the String Quartet. In the last movement of the concerto, similarities to the halling (a Norwegian folk dance) and imitations of the Hardanger fiddle (the Norwegian folk fiddle) have been detected.
The work was premiered by Edmund Neupert on April 3, 1869 in Copenhagen, with Holger Simon Paulli conducting. Some sources say that Grieg himself, an excellent pianist, was the intended soloist, but was unable to attend the premiere owing to commitments with an orchestra in Christiania (now Oslo). Among those who did attend the premiere were the Danish composer Niels Gade and the Russian pianist Anton Rubinstein, who provided his own piano for the occasion. Neupert was also the dedicatee of the second edition of the concerto (Rikard Nordraak was the original dedicatee), and it was said that he himself composed the first movement cadenza.
The Norwegian premiere in Christiania followed on August 7, 1869, and the piece was later heard in Germany in 1872 and England in 1874. At Grieg's visit to Franz Liszt in Rome in 1870, Liszt played the notes a prima vista before an audience of musicians and gave very good comments on Grieg's work, which influenced him later. The work was first published in Leipzig in 1872, but only after Johan Svendsen intervened on Grieg's behalf.
The concerto is the first piano concerto ever recorded — by pianist Wilhelm Backhaus in 1909. Due to the technology of the time, it was heavily abridged at only six minutes.
Grieg revised the work at least seven times, usually in subtle ways, but amounting to over 300 differences from the original orchestration. In one of these revisions, he undid Franz Liszt's suggestion to give the second theme of the first movement (as well as the first theme of the second) to the trumpet rather than to the cello. The final version of the concerto was completed only a few weeks before Grieg's death, and it is this version that has achieved worldwide popularity. The original 1868 version has been recorded, by Love Derwinger, with the Norrköping Symphony Orchestra under Jun'ichi Hirokami.
Grieg worked on a transcription of the concerto for two solo pianos, which was completed by Károly Thern. The premiere recording of this version was by the British two-piano team of Anthony Goldstone and Caroline Clemmow
On April 2, 1951, Russian-born American pianist Simon Barere collapsed while playing the first few bars of the concerto, in a performance with conductor Eugene Ormandy and the Philadelphia Orchestra at Carnegie Hall in New York. He died backstage shortly afterwards. It was to have been Barere's first performance of the work.
In 1882–83 Grieg worked on a second piano concerto in B minor, but it was never completed. The sketches for the concerto have been recorded by pianist Einar Steen-Nøkleberg. In 1997, the Belgian composer Laurent Beeckmans elaborated a full piano concerto from these sketches that was first performed in London on 3rd May 2003.