Quantitative ultrasound (QUS), which attempts to extract quantitative features from the US radiofrequency (RF) or envelope data for tissue characterization, is becoming a promising technique for noninvasive assessments of liver fibrosis. However, the number of feature variables examined and finally used in the existing QUS methods is typically small, limiting the diagnostic performance. Therefore, this paper devises a new multiparametric QUS (MP-QUS) method which enables the extraction of a large number of feature variables from US RF signals and allows for the use of feature-engineering and machine-learning based algorithms for liver fibrosis assessment. In the MP-QUS, eighty-four feature variables were extracted from multiple QUS parametric maps derived from the RF signals and the envelope data. Afterwards, feature reduction and selection were performed in turn to remove the feature redundancy and identify the best combination of features in the reduced feature set. Finally, a variety of machine-learning algorithms were tested for fibrosis classification with the selected features, based on the results of which the optimal classifier was established. The performance of the proposed MP-QUS method for staging liver fibrosis was evaluated on an animal model, with histologic examination as the reference standard. The mean accuracy, sensitivity, specificity and area under the receiver-operating-characteristic curve achieved by MP-QUS are respectively 83.38%, 86.04%, 80.82%, and 0.891 for recognizing significant liver fibrosis, and 85.50%, 88.92%, 85.24%, and 0.924 for diagnosing liver cirrhosis. The proposed MP-QUS method paves a way for its future extension to assess liver fibrosis in human subjects.