Abstract: This paper gives an option pricing algorithm based on Fourier transform. Compared with other similar algorithms that have been published, our algorithm has more advantages including faster convergence, shorter time of execution and easier implementation by computer programming. On the one hand, we theoretically show the effectiveness of our algorithm through the relationship between function smoothness and its decay rate at tail. On the other hand, the numerical calculations we conducted for European options and digital options with three model types of underlying assets further support the effectiveness from the perspective of empirical analysis.