The technique of non-invasive cortical bone quality assessment using ultrasound axial transmission has attracted considerable attention. Estimating the phase velocity and the attenuation of the absorbing plate will assist the assessment. Among several techniques proposed for these purposes, many employ either a thresholding process or a peak search process. The thresholding process uses the intensity of the guided wave to distinguish the noise from the signal, but may dismiss weak intensity modes. The peak search process extracts the phase velocity and attenuation from the estimated intensity in the frequency and wavenumber domains; however, this process costs a large computational load. To overcome these difficulties, we propose a novel algorithm that uses an adaptive beamforming technique.