This paper is devoted to studying the fast numerical method for convolutiontype Volterra integral equation of the first kind. High order numerical schemes are devised by using special multistep collocation methods, which depend on numerical approximations of the solution in the next several steps. Then the original integral equation is discretized into a system of linear equations, and the coefficient matrix can be decomposed into a Toeplitz matrix and a sparse matrix. The fast calculation of linear equations is implemented by using fast Fourier transform in this paper, and the calculation amount is O（NlogN）. Numerical examples are provided to demonstrate the efficiency of the proposed method.