Amlaíb mac Illuilb was a tenth-century King of Alba. He was one of three sons of Illulb mac Custantín, King of Alba, and a member of Clann Áeda meic Cináeda, a branch of the Alpínid dynasty. Amlaíb's paternal grandfather possessed strong connections with the Scandinavian dynasty of Dublin, and there is evidence to suggest that Illulb and Amlaíb bore names of Old Norse origin. If Amlaíb's name indeed represents a Gaelicised Scandinavian name, it could be evidence that his mother was a member of the Uí Ímair, and possibly a granddaughter of Amlaíb Cúarán or Amlaíb mac Gofraid.
Following Illulb's death in 962, the kingship of Alba was taken up by Dub mac Maíl Coluim, a member of Clann Custantín meic Cináeda, a rival branch of the Alpínid dynasty. This king soon faced opposition from Amlaíb's brother, Cuilén, before the latter secured the kingship for himself in 966. Cuilén and another son of Illulb were slain in 971, after which the kingship was taken up by Dub's brother, Cináed mac Maíl Choluim. According to Irish sources, the latter slew Amlaíb in 997. The fact that these sources style Amlaíb as a king, and fail to accord a royal title to Cináed, suggests that Amlaíb was successful in seizing the kingship from his rival. Amlaíb's short reign appears to date to 971/976–977.