Olaf I (Danish: Oluf; c. 1050 – 18 August 1095), nicknamed Olaf Hunger, was king of Denmark from 1086 to 1095, following the death of his brother Canute IV the Holy. He was a son of king Sweyn II Estridsson, and the third of Sweyn's sons to rule. He married Ingegard, the daughter of Harald Hardråde, but did not have any children. He was succeeded by his brother Eric I Evergood.

Olaf was born around 1050, to king Sweyn II Estridsson and an unknown concubine. During the reign of his elder brother Canute IV, Olaf supposedly served as Duke of Schleswig. In 1085, Olaf was called to a leding campaign against England. Canute was held up and could not join the leding, and as the navy grew weary in waiting for him, Olaf became the spokesperson for its concerns. Canute feared Olaf's support among the magnates, while Olaf had misgivings about Canute's dynastic ambition, and saw Canute's son Charles the Good as a potential rival for power. Canute blamed Olaf for stirring up trouble, and Olaf was put in chains by their brother Eric, the later king Eric I Evergood. Olaf was banished to Flanders, under the supervision of Robert I of Flanders.

Canute was killed in St. Alban's Priory in Odense in July 1086, following a rebellion in Northern Jutland. Olaf was proclaimed king at the Viborg landsting assembly, though he was still in Flanders. An arrangement was made to swap Olaf for his younger brother Niels, the later king Niels of Denmark, to permit Olaf to return to Denmark. Upon the return of Oluf, Eric fled to Scania. Olaf was the third of Sweyn's sons to become king of Denmark.

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