This paper proposes a novel self-supervised learning method, RELAX-MORE, for quantitative MRI (qMRI) reconstruction. The proposed method uses an optimization algorithm to unroll a model-based qMRI reconstruction into a deep learning framework, enabling the generation of highly accurate and robust MR parameter maps at imaging acceleration. Unlike conventional deep learning methods requiring a large amount of training data, RELAX-MORE is a subject-specific method that can be trained on single-subject data through self-supervised learning, making it accessible and practically applicable to many qMRI studies. Using the quantitative mapping as an example at different brain, knee and phantom experiments, the proposed method demonstrates excellent performance in reconstructing MR parameters, correcting imaging artifacts, removing noises, and recovering image features at imperfect imaging conditions. Compared with other state-of-the-art conventional and deep learning methods, RELAX-MORE significantly improves efficiency, accuracy, robustness, and generalizability for rapid MR parameter mapping. This work demonstrates the feasibility of a new self-supervised learning method for rapid MR parameter mapping, with great potential to enhance the clinical translation of qMRI.