Disclosed are a memristor element, a synapse element and a neuromorphic processor including the same. The memristor element includes a free layer including a domain wall; and a fixed layer including a material of which a magnetization direction is fixed, wherein a position of the domain wall in the free layer is changeable based on a spin orbit torque (SOT) generated by a current introduced from an outside, and wherein a resistance value, measured through both ends of the fixed layer, is based on the position of the domain wall and on a Hall voltage.