In this paper, the authors study the multidegree reduction of Bézier curves with arbitrary degree interpolation conditions of two endpoint. For the given endpoint interpolation conditions, a new approximation method of multidegree reduction is presented. Using Chebyshev polynomial approximation theory, the nearly best uniform approximation under the interpolation conditions of endpoints can be obtained. This algorithm is easy to implement and simple for error estimation. The approximation effects of the degree reduction curves are very good. Combined with subdivision algorithm, it can reach a higher rate of error convergence.