This paper proposes the technique of estimating the pipe thickness using the measured group velocity. To measure the group velocity from the accelerometer data in the frequency domain, Wigner-Ville distribution is utilized, which interprets the waveform of the shock wave. Using this measured group velocity, this paper proposes the technique to estimate the thickness of pipes with the impact on the pipe. The group velocity is estimated by the modeling correlation between the group velocity and the thickness of the pipe based on the propagation velocities. The correlation model between thickness and group velocity has been proved through the real experiments. The measured group velocity in the frequency-domain is the maximum at the center frequency of the bending waves in the modeling of the group velocity. In addition to these, a smoothing technique for analyzing lamb wave Wigner-Ville distribution has been introduced to improve the reliability of the data acquisition.