Due to velopharyngeal incompetence, airflow overflows from the oral cavity to the nasal cavity, which results in hypernasality. Hypernasality greatly reduces speech intelligibility and affects the daily communication of patients with cleft palate. Accurate assessment of hypernasality grades can provide assisted diagnosis for speech-language pathologists (SLPs) in clinical settings. Utilizing a support vector machine (SVM), this paper classifies speech recordings into four grades (normal, mild, moderate and severe hypernasality) based on vocal tract characteristics. Linear prediction (LP) analysis is widely used to model the vocal tract. Glottal source information may be included in the LP-based spectrum. The stabilized weighted linear prediction (SWLP) method, which imposes the temporal weights on the closed-phase interval of the glottal cycle, is a more robust approach for modeling the vocal tract. The extended weighted linear prediction (XLP) method weights each lagged speech signal separately, which achieves a finer time scale on the spectral envelope than the SWLP method. Tested speech recordings were collected from 60 subjects with cleft palate and 20 control subjects, and included a total of 4640 Mandarin syllables. The experimental results showed that the spectral envelope of normal speech decreases faster than that of hypernasal speech in the high-frequency part. The experimental results also indicate that the SWLP- and XLP-based methods have smaller correlation coefficients between normal and hypernasal speech than the LP method. Thus, the SWLP and XLP methods have better ability to distinguish hypernasal from normal speech than the LP method. The classification accuracies of the four hypernasality grades using the SWLP and XLP methods range from 83.86% to 97.47%. The selection of the model order and the size of the weight function are also discussed in this paper.