Quantitative functional magnetic resonance imaging (fMRI) requires reliable mapping of brain function in task-or resting-state. In this work, a spatially regularized support vector machine (SVM)-based technique was proposed for brain functional mapping of individual subjects and at the group level. Unlike most SVM-based fMRI data analysis approaches that conduct supervised classifications of brain functional states or disorders, the proposed technique performs a semi-supervised learning to provide a general mapping of brain function in task-or resting-state. The method can adapt to between-session and between-subject variations of fMRI data, and provide a reliable mapping of brain function. The proposed method was evaluated using synthetic and experimental data. A comparison with independent component analysis methods was also performed using the experimental data. Experimental results indicate that the proposed method can provide a reliable mapping of brain function and be used for different quantitative fMRI studies.