Brain functional connectivity (FC) has shown great potential in becoming biomarkers of brain status. However, the problem of accurately estimating FC from complex-noisy fMRI time series remains unsolved. Usually, a regularization function is more appropriate in fitting the real inherent properties of the brain function activity pattern, which can further limit noise interference to improve the accuracy of the estimated result. Recently, the neuroscientists widely suggested that the inherent brain function activity pattern indicates sparse, modular and overlapping topology. However, previous studies have never considered this factual characteristic. Thus, we propose a novel method by the integration of these inherent brain function activity pattern priors to estimate FC. Extensive experiments on synthetic data demonstrate that our method can more accurately estimate the FC than previous. Then, we applied the estimated FC to predict the symptom severity of depressed patients, the symptom severity is related to subtle abnormal changes in the brain function activity, a more accurate FC can more effectively capture the subtle abnormal brain function activity changes. As results, our method better than others with a higher correlation coefficient of 0.4201. Moreover, the overlapping probabilistic of each brain region can be further explored by the proposed method.