Quantitative R2* map is an important liver disease indicator. However, the availability of R2* map is limited by the long scan time. In this study, we present a new paradigm to predict R2* and B0 maps from dual echo images. A self-attention deep convolutional neural network is trained and validated, where promising accuracy has been obtained. The proposed quantitative parametric mapping approach has a potential to eliminate the necessity for additional data acquisition other than clinical routine.