Specific patterns of lung ultrasound images are utilized to assess the severity of COVID-19 pneumonia, while such assessment is mainly based on clinicians' qualitative and subjective observations. In this study, we quantitatively analyze the LUS images to assess the severity of COVID-19 pneumonia by characterizing the patterns related to the pleural line and B-lines. 27 patients with COVID-19 pneumonia, including 13 moderate cases, 7 severe cases, and 7 critical cases, are enrolled. Features related to the pleural line, including the thickness (TPL) and roughness of the pleural line (RPL), and the mean (MPLI) and standard deviation (SDPLI) of the pleural line intensities are extracted from the LUS images. Features related to the B-lines, including the number (NBL), accumulated width (AWBL), attenuation coefficient (ACBL), and accumulated intensity (AIBL) of B-lines are also extracted. The correlations of these features with the disease severity are evaluated. The performances of the binary severe / non-severe classification are assessed for each feature and support vector machine (SVM) classifiers with various combinations of features as input. Several features, including the RPL, NBL, AWBL, and AIBL show significant correlations with disease severity (all p < 0.05). The classification performance is optimal by employing the SVM classifier using all the features as input (area under the receiver operating characteristic curve = 0.96, sensitivity = 0.93, specificity = 1). These findings demonstrate that the proposed method may be a promising tool for automatic grading diagnosis and follow-up of patients with COVID-19 pneumonia.