Abstract: The recently developed on-surface discretized boundary equation （OS-DBE） method for scattering by a conducting cylinder allows an independent determination of the current density at any given point on the object surface with a matrix of smaller order than that in the method of moments. This paper incorporates the asymptotic waveform evaluation technique into the OS-DBE method to the fast spatial sweep calculation to generate the whole current distribution, reduces the number of current calculation points at which the utilization of the OS-DBE is necessary and improves the numerical efficiency. Besides, numerical results are Presented to demonstrate the validity and efficiency of the proposed technique compared to the method of moment （MoM）.