Sweyn Asleifsson or Sveinn Ásleifarson (c. 1115 – 1171) was a twelfth-century Viking who appears in the Orkneyinga Saga.
Sweyn was born in Caithness in the early twelfth century, to Olaf Hrolfsson and his wife Åsleik. According to the Orkneyinga Saga, he came to prominence when he murdered Earl Paul of Orkney's cup-bearer c. 1134 in a quarrel over a drinking game, and fled to Tiree to take refuge with Holdbodi Hundason.
In 1140, Holdbodi called on Sweyn to join him raiding the coast of Wales, but they were beaten off, Holdbodi withdrawing to the Isle of Man and Sweyn to Lewis. In the early summer of 1141, Sweyn arrived in Man to join Holdbodi, but the Hebridean had been persuaded to join forces with the Norman-Welsh lord Robert who had defeated them in the previous year, and attacked Sweyn. This created a feud between the former friends.
Some years later, after falling out with his own captains (led by his brother-in-law Thorbjorn Thorsteinsson), Sweyn was driven out of Orkney by Rognvald Kali Kolsson, but King David I persuaded them to make peace.
Olvir Rosta killed Sweyn's father; later Sweyn attacked Olvir, killed his grandmother, and Olvir fled to the Hebrides.
In 1153, there was a falling-out between the three Earls of Orkney (Rognvald Kali Kolsson, Erlend Haraldsson and Harald Maddadsson). Sweyn, backed by the new King, Malcolm IV, threw in his lot with Erlend, attacking the shipping of the other two Earls and raiding the east coast of Scotland in his company.