In this paper we present fast discrete collocation methods for Volterra integral equations of Hammerstein type, where the Laplace transform of the kernel is known a priori. To compute the numerical solution over N t time steps, the constructed methods require O ( N t log ( N t ) ) operations, O ( log ( N t ) ) memory and preserve the order of accuracy of the corresponding exact collocation methods. The numerical experiments confirm the expected accuracy and the computational cost.