As revealed in Halloween: The Curse of Michael Myers, a group of druids belonging to Halloween's Cult of Thorn placed a curse on Michael when he was an infant. This curse causes him to be possessed by Thorn, a demonic force that requires its host to sacrifice their family on Samhain (now known as Halloween night).
A couple of years after Judith's murder, Michael Myers' parents died in a car accident, and Laurie was put into foster care, where she was immediately adopted by the Strode family. It's unknown how Michael knew Laurie Strode was his sister, but this gave him a somewhat clearer reason to go after her.