A steering damper control apparatus includes an MR damper 45 having an adjustable steering damping force, a suspension pressure sensor 41 for detecting a pressure of a front suspension, a command value output unit 81 for determining a damping force command value according to a pressure change rate of the front suspension 40 based on a detection result of the suspension pressure sensor 41, and a damper driver 77 for causing the MR damper 45 to generate a damping force corresponding to the damping force command value. At a point of time when steering has become easily shakable, the damping force corresponding to the damping force command value can be generated to inhibit shaking of the steering beforehand.