The Lubich coefficient is investigated from the point of view of signal processing, and the frequency characteristics of Lubich coefficient are analyzed. A fast algorithm based on Inverse Fast Fourier Transform (IFFT) for computing Lubich coefficient is designed. The Lubich coefficient directly solved by IFFT algorithm is not accurate. The Gibbs effect exists in the frequency domain with low order operations, and the new algorithm can reduce this effect effectively by zero-frequency assignment. The numerical simulation results show that, compared with Lubich accuracy coefficient, the Lubich approximation coefficients computed by the new algorithm have better performance in constructing the digital fractional differentiator with a certain proper fraction operation order range, and the new algorithm has low computational complexity and high efficiency.