Phase-change memory, which switches reversibly between crystalline and amorphous phases, is promising for next generation data-storage devices. In this work, we present a novel, nonbinary data-storage device using core-shell nanowires to significantly enhance memory capacity by combining two phase-change materials with different electronic and thermal properties to engineer different onsets of amorphous-crystalline transitions. Electric-field induced sequential amorphous-crystalline transition in core-shell nanowires displays three distinct electronic states with high, low, and intermediate resistances, assigned as data "0", "1", and "2".