Multi-echo saturation recovery sequence can provide redundant information to synthesize multi-contrast magnetic resonance imaging. Traditional synthesis methods, such as GE's MAGiC platform, employ a model-fitting approach to generate parameter-weighted contrasts. However, models' over-simplification, as well as imperfections in the acquisition, can lead to undesirable reconstruction artifacts, especially in T2-FLAIR contrast. To improve the image quality, in this study, a multi-task deep learning model is developed to synthesize multi-contrast neuroimaging jointly using both signal relaxation relationships and spatial information. Compared with previous deep learning-based synthesis, the correlation between different destination contrast is utilized to enhance reconstruction quality. To improve model generalizability and evaluate clinical significance, the proposed model was trained and tested on a large multi-center dataset, including healthy subjects and patients with pathology. Results from both quantitative comparison and clinical reader study demonstrate that the multi-task formulation leads to more efficient and accurate contrast synthesis than previous methods.