A steer by wire apparatus performing steering operation by turning a wheel when a vehicle turns, may include a tie rod provided with one end pivotally connected to a knuckle of the wheel, a coupling unit rotatably mounted at a sub-frame of a vehicle body, connected to the other end of the tie rod, and converting rotation direction of torque from a first rotation direction to a second rotation direction which is substantially perpendicular to the first rotation direction so as to slidably move the tie rod from the coupling unit and control a steering angle of the wheel, and a motor unit fixed to the sub-frame and supplying the torque to the coupling unit according to a control signal of a vehicle ECU, the rotation direction of the torque being the same as the first rotation direction or being opposite to the first rotation direction.