Abstract: A new fast algorithm for calculating the coefficients of ideal digital fractional differentiator is presented. It is difficult to compute directly the coefficients from the integral formula, since the integral function in the formula of the ideal digital fractional differentiator is a high-order oscillating function. Based on the properties of the integral formula, it's easy to convert the oscillating factor to the integral upper limit. Therefore a set of recursive expressions for calculating coefficients of ideal digital fractional differentiator are introduced in this paper. The experimental result shows that the new algorithm decreases the amount of operation greatly, at the same time promotes the algorithm's efficiency as well as avoid integral of high-order oscillating function.