Grünenberg was perhaps born around 1415 or earlier, as the son of the mayor of Constance. He is first mentioned in 1441 as a judge and church architect. By 1465, he had been in the service of Emperor Frederick III for some time, and at the latest 1486 on held the rank of Ritter. In Jerusalem, he was probably made a Knight of the Holy Sepulchre. He was furthermore a member of the Aragonese Order of the Jar and of the Austrian Order of Saint George.
His pilgrimage to the Holy Land lasted 33 weeks, from April to early December 1486. Starting out in Constance on 22 April, he travelled to Venice via Rheineck, Sterzing in Tyrol and Trento, and from Venice by galley via Poreč in Istria, Dalmatia to Corfu, Modon in Morea, then on to Candia on Crete, Rhodes, and Cyprus, arriving in Jaffa on 24 July. Travelling by donkey, he visited Lydda, Ramla, Emmaus, Jerusalem and Bethlehem. On 1 September he took a ship back from Jaffa, reaching Venice on 16 November, returning home in early December. The two original illustrated manuscripts describing the pilgrimage were already completed in 1487 and are considered to be autograph. The slightly older one is being kept at the Baden State Library in Karlsruhe as Cod. St. Peter pap. 32; and the next and more detailed one is being kept at the Gotha Research Center of the University of Erfurt. Both codices contain coloured drawings, and while some of the drawings in the Karlsruhe codex seem to be made by Grünenberg himself, the Gotha codex is illustrated with larger drawings that combine features of the Karlsruhe drawings with features borrowed from Erhard Reuwich's work, originating from Reuwich's own 1483-4 pilgrimage. The Karlsruhe codex has been interpreted as Grünenberg's own private copy, with the Gotha codex, which contains a more elaborate text and more detailed drawings, interpreted as a presentation copy dedicated to some important personality.
Revised and facsimile editions
Stillfried-Alcantara, Hildebrandt, Des Conrad Grünenberg, Ritters und Burgers zu Costenz, Wappenbuch. Volbracht am nünden Tag des Abrellen do man zalt tusend vierhundert drü und achtzig jar. Görlitz 1875–1884,
Johann Goldfriedrich, Walter Fränzel. Ritter Grünembergs Pilgerfahrt ins Heilige Land 1486, Leipzig 1912,,.
Aercke, Kristian, The story of Sir Konrad Grünemberg's pilgrimage to the Holy Land in 1486.