Nonalcoholic fatty liver disease (NAFLD) affects ~25% of the world population. Confounder-corrected chemical-shift-encoded MRI-derived proton density fat fraction (MRI-PDFF) is an established quantitative noninvasive biomarker of hepatic steatosis but has limited availability. There is a clinical need for more practical and accessible methods to noninvasively assess hepatic steatosis. Previous work has shown that two quantitative ultrasound (QUS) biomarkers - attenuation coefficient (AC) and backscatter coefficient (BSC) - are correlated with hepatic steatosis. Examining a broad range of QUS biomarkers, this study aims to develop an improved, multi-parametric QUS-based approach to diagnose NAFLD and quantify hepatic fat, with MRI-PDFF as the reference standard. 102 participants recruited from the UCSD NAFLD Research Center underwent QUS exams on the right liver lobe with an Acuson S3000 ultrasound scanner and the 4C1 and 6C1HD transducers. Seven QUS biomarkers - AC, BSC, three Lizzi-Feleppa parameters (slope, intercept, midband), and two envelope parameters (k and μ) - were derived from ultrasound radiofrequency data. Two multivariable models were developed based on QUS biomarkers: a generalized linear regression model to predict hepatic PDFF using stepwise regression for biomarker selection and a regularized logistic regression model to classify NAFLD (MRI-PDFF>5%, N=78/102) versus no NAFLD (MRI-PDFF≤5%) using LASSO regularization for biomarker selection. Leave-one-out cross-validation was performed. The final regression model selected the midband and k-parameter. The cross-validated predicted PDFF values were correlated with the reference MRI-PDFF values (Spearman ρ = 0.82 and Pearson's r = 0.76). In comparison, Pearson's r was 0.59 between AC and MRI-PDFF and 0.58 between BSC and MRI-PDFF. The final classifier model selected the midband, k-parameter and μ-parameter, achieving an area under the receiver operating characteristic curve (AUROC) of 0.88. In comparison, AUROC was 0.83 using AC and 0.84 using BSC. The results suggest that multi-parametric QUS can improve the quantification of hepatic steatosis and diagnosis of NAFLD.