Abstract: A high precision numerical algorithm was designed to compute fractional-order derivative and integral， and a simple method was proposed to construct the generating function. An algorithm based on fast Fourier transform was analyzed. It could be concluded that the reasons of its large computation error were using the inaccurate coefficient of the generating function and no considering the effect of nonzero initial condition of the original function on calculation precision. The recursive formula was used to compute the coefficient of the generating function in the new algorithm， what’s more， the original function was decomposed into two parts， i.e.， zero initial condition and nonzero initial condition， and their fractional-order derivative and integral were computed to decrease the computation error. The error analysis and the illustrative numerical examples showed that the computation accuracy of the new algorithm was very high.

Key words: fractional-order, derivative and integral, generating function, high-precision, recursive algorithm