Adolf Jensen was born in 1837 in Königsberg. His family were musicians. He mostly taught himself music but he got help from Louis Ehlert, Louis Köhler and Friedrich Marpurg (1825–1884). Ehlert came from Königsberg, Köhler taught there, and Marpurg was the director of the Königsberg Theater and the great grandson of Friedrich Wilhelm Marpurg who wrote books about music theory. In 1856 he went to Russia to teach. He wanted to make money so he could take lessons with Robert Schumann but Schumann died. In 1857 he was the music director of the Posen City Theater. From 1858 until 1860 he lived in Copenhagen and he made friends with Niels Gade. Then he went back to Königsberg and composed a lot of his music then. He went to Berlin and taught advanced piano at Carl Tausig's "Schule des höherin Clavierspiels" from 1866 until 1868. Then he got very sick and had to retire. He went to Dresden, and then to Graz in 1870 and then to Baden-Baden. He died there of tuberculosis in 1879 when he was 42.
Jensen wrote about 160 songs, and music for choir. His music for piano includes a Sonata in F sharp minor (Op. 25), a set of 25 Études (Op. 32), and Erotikon, Op. 44, seven pieces depicting scenes from Greek legends. He also wrote music for piano four hands.
His orchestral music consisted of a Concert Overture in E minor and a Geistliches Tonstück. He started work on opera Die Erbin von Montfort in 1864-65, but never finished it. After his death, Wilhelm Kienzl adapted the music to a new libretto, Turandot, written by Jensen's daughter Elsbeth, who wrote under the pseudonym "Egbert Jensen".