This paper develops a structured low rank approximation (SLRA) method for noise elimination from a noisy impulsive response function (IRF). Cadzow’s algorithm is implemented for the SLRA on the Hankel matrix constructed by measured IRF in order to obtain a filtered IRF. Using the proposed noise elimination scheme, some important factors, such as the size of a Hankel matrix and the quantification of the noise reduction performance are evaluated. Synthesized IRFs are applied to demonstrate the performance, and illustrate the procedure as well, of the proposed scheme in the numerical study. The results indicate that this method can eliminate noise from measured IRFs efficiently.