If the wave mode used in guided wave non-destructive inspection is dispersive, reflected pulses from damaged parts may be significantly distorted due to wave dispersion. The main concern, in this case, is how to detect the reflected pulses in noisy signals, and to extract meaningful damage information from the detected pulses. However, current signal processing techniques used for guided wave inspection do not account for pulse dispersion, so the extracted information is often not so accurate. The objective of this study is to develop an efficient technique to deal with dispersed pulses for guided-wave nondestructive evaluation. Our idea is to model dispersed pulses by chirp functions of special form that can simulate up to quadratically varying group delay. To determine the parameters of the chirp functions approximating dispersed, reflected pulses, an adaptive matching pursuit algorithm is employed. Once the characterizing parameters are found, the damage location and extent can be estimated. The proposed method is tested with experimentally measured signals of longitudinal waves in a circular cylinder.