The dispersive phase velocity of a wave propagating through multilayered systems such as a soil site is an important parameter and carries valuable information in non-destructive site characterization tests. The dispersive phase velocity of a wave can be determined using the phase spectrum, which is easily evaluated through the cross power spectrum. However, the phase spectrum determined using the cross power spectrum is easily distorted by background noise which always exists in the field. This causes distortion of measured signal and difficulties in the determination of the dispersive phase velocities. In this paper, a new method to evaluate the phase spectrum using the harmonic wavelet transform is proposed and the phase spectrum by the proposed method is applied to the determination of dispersion curve. The proposed method can successfully remove background noise effects. To evaluate the validity of the proposed method, numerical simulations of multi-layered systems were performed. Phase spectrums and dispersion curves determined by the proposed method were found to be in good agreement with the actual phase spectrums and dispersion curves biased by heavy background noise. The comparison manifests the proposed method to be a very useful tool to overcome noise effects.