T1 maps from fast field-cycling (FFC) MRI can provide insights to structural information and dynamics of molecular system not accessible by traditional MRI. The low SNR associated with the lower field strength in FFC imaging (0.2 T - 50 µT) leads to long acquisition times, impairing its clinical applicability. Hence, we propose a model-based reconstruction strategy to reduce acquisition time and improve image quality of multi-field T1 maps. The method is compared to standard fitting on numerical phantoms and a in vivo stroke patient. Model-based reconstruction clearly outperformed standard fitting, reducing noise and revealing previously unseen details in low-field T1 maps.