Hepatocellular Carcinoma (HCC) detection, size grading, and quantification (i.e. the center point coordinates, max-diameter, and area) by using multi-modality magnetic resonance imaging (MRI) are clinically significant tasks for HCC assessment and treatment. However, delivering the three tasks simultaneously is extremely challenging due to: 1) the lack of effective an mechanism to capture the relevance among multi-modality MRI information for multi-modality feature fusion and selection; 2) the lack of effective mechanism and constraint strategy to achieve mutual promotion of multi-task. In this paper, we proposed a task relevance driven adversarial learning framework (TrdAL) for simultaneous HCC detection, size grading, and multi-index quantification using multi-modality MRI (i.e. in-phase, out-phase, T2FS, and DWI). The TrdAL first obtains expressive feature of dimension reduction via using a CNN-based encoder. Secondly, the proposed modality-aware Transformer is utilized for multi-modality MRI features fusion and selection, which solves the challenge of multi-modality information diversity via capturing the relevance among multi-modality MRI. Then, the innovative task relevance driven and radiomics guided discriminator (Trd-Rg-D) is used for united ad-versarial learning. The Trd-Rg-D captures the internal high-order relationships to refine the performance of multi-task simultaneously. Moreover, adding the radiomics feature as the prior knowledge into Trd-Rg-D enhances the detailed feature extraction. Lastly, a novel task interaction loss function is used for constraining the TrdAL, which enforces the higher-order consistency among multi-task labels to enhance mutual promotion. The TrdAL is validated on a corresponding multi-modality MRI of 135 subjects. The experiments demonstrate that TrdAL achieves high accuracy of (1) HCC detection: specificity of 93.71%, sensitivity of 93.15%, accuracy of 93.33%, and IoU of 82.93%; (2) size grading: accuracy of large size, medium size, small size, tiny size, and healthy subject are 90.38%, 87.74%, 80.68%, 77.78%, and 96.87%; (3) multi-index quantifi-cation: the mean absolute error of center point, max-diameter, and area are 2.74mm, 3.17mm, and 144.51mm 2. All of these results indicate that the proposed TrdAL provides an efficient, accurate, and reliable tool for HCC diagnosis in clinical.