To provide a steering damping apparatus for a vehicle, which is capable of easily performing handling of steering during upright traveling and restraining a falling accident from occurring by performing excessive steering during cornering.

The steering damping apparatus for the vehicle includes a car body tilting angle detector 31, a steering angle detector 32 and a control unit which controls operation characteristics of a steering damper 1 for both the detected tilting angle and steering angle of a car body. The operation characteristics of the steering damper 1 are controlled in such a manner that: while the steering angle is in a neutral steer area with respect to each of detected tilting angles of the car body, braking force to be operated on steering members 9 and 9 is weakened; and while the steering angle is out of the neutral steer area with respect to each of tilting angles of the car body, the braking force to be operated on the steering members 9 and 9 is made stronger as a degree at which the steering angle is out of the neutral steer area becomes greater.