Motion capturing is widely used for generating realistic motions. A 3D input device captures a sequence of 6 DOF rigid motion samples. The sampled data consist of two components, translation and orientation; the former is represented by a vector in R3 and the latter by a rotation matrix in the rotation group, SO(3). Since the sequence of data contain sampling noises, the captured motion is not smooth and wiggles along the moving path. There are well-known fairing algorithms in Euclidean space based on difference geometry. Extending these for the motion data, we present a new fairing algorithm. The new algorithm iteratively minimizes the energy function reflecting the forces and torques, exerted on a moving object, to perform motion fairing.