Abstract: The Volterra filtering is an effective method in nonlinear adaptive signal processing. However its very high computational complexity renders the applications of the Volterra filtering in practice rather limited. To overcome this drawback, this paper presents a fast algorithm for the Volterra filtering which can significantly relieve the computational burden. The complexities of the fast algorithm and the original one are analyzed and compared. A simulation example is also given which uses the Volterra adaptive model for modelling unknown nonlinear systems.