The interpolation of some given moving frames (origin position+orientations of three coordinate axes) of a moving object is an important problem in the fields of computer graphics, robotics, etc. In this paper, a new method is presented to interpolate and approximate the moving frames of moving object by employing B-splines. By parameterizing the rotation transformation part of the orthogonal moving frame with four Euler parameters, a simplified optimization function is derived. An iteration method is presented to solve the optimization function for approximating the rotation transformation part of the pseudo moving frame at any position of the motion trajectory. The error caused by interpolation and approximation is proven to be controllable. Since the computation of moving frame is only related with order 2 or 3 linear equations, the proposed approach can be implemented with high efficiency.