Provided is a magnetorheological (MR) damper, which includes a cylinder filled with an MR fluid, a piston rod extending to the outside of the cylinder, and a magnetic generator partitioning the inside of the cylinder into a compression chamber and a rebound chamber in a state of being connected to the piston rod and generating an electromagnetic force to the inside, the MR damper including: a magnetic core connected to a lower end of the piston rod; a flux ring connected to an edge of the magnetic core, such that a side surface of the flux ring tightly contacts an inner peripheral surface of the cylinder, the flux ring being formed to vertically penetrate through a main passage between the flux ring and the magnetic core; and a cutaway groove concavely formed at a side surface of the magnetic core and preventing a magnetic force from being unnecessarily formed at a setting portion of the main passage, such that the MR fluid is vertically bypassed during compression and rebound strokes.