Recently, inference of functional connectivity between brain regions using resting state fMRI (rsfMRI) data has attracted significant interests in the neuroscience community. This paper proposes a novel fiber-centered approach to study the functional connectivity between brain regions using high spatial resolution diffusion tensor imaging (DTI) and rsfMRI data. We measure the functional coherence of a fiber as the time series' correlation of two gray matter voxels that this fiber connects. The functional connectivity strength between two brain regions is defined as the average functional coherence of fibers connecting them. Our results demonstrate that: 1) The functional coherence of fibers is correlated with the brain regions they connect; 2) The functional connectivity between brain regions is correlated with structural connectivity. And these two patterns are consistent across subjects. These results may provide new insights into the brain's structural and functional architecture.