Ultrasound bone evaluation is of great significance for the diagnosis and prevention of metabolic bone disease in neonates. Dual-energy X-ray absorptiometry, a routine clinical technique, is difficult to meet the clinical needs of long-term monitoring of neonatal bone status due to ionizing radiation. Biochemical index testing, as an invasive detection method, is likewise unsuitable for evaluating neonatal bone status. Ultrasonic guided wave detection technology, with its advantages of non-invasiveness and absence of ionizing radiation, has been applied to the diagnosis of osteoporosis and fracture evaluation. However, clinical research on applying ultrasonic guided waves to evaluate neonatal cortical bone quality still needs further development. To address this issue, we propose an ultrasonic guided wave wavenumber dispersion extraction method based on the Matrix Pencil spectral estimation, aiming to achieve accurate evaluation of the sound velocity and cortical thickness of the neonatal tibia. First, a single-layer bone plate model and a multi-channel ultrasonic phased array guided wave field were constructed through numerical simulation. Experimental results showed that the relative errors of thickness assessment for isotropic plates with thicknesses of 1, 2, and 4 mm were all less than 3%. A horizontal comparison of cortical thickness assessment results under signal-to-noise ratios of 10 and 5 dB verified that the evaluation accuracy was less affected by noise. Furthermore, this wavenumber dispersion extraction method was applied to evaluate the longitudinal wave velocity in neonatal tibial cortical bone. The results indicated that the relative error between the estimated cortical sound velocity and the clinical ultrasonic measurement results was less than 10%, and the detected cortical thickness was significantly correlated with various neonatal physical measurement values (p-value < 0.001). This study demonstrates the clinical application value of the ultrasonic guided wave method in assessing neonatal tibia bone quality and effectively expands its scope of application in clinical practice.