Synchronized low-frequency spontaneous fluctuations of the functional MRI (fMRI) signal have been shown to be associated with electroencephalography (EEG) power fluctuations in multiple brain networks within predefined frequency bands. However, it remains unclear whether frequency-specific characteristics exist in the resting-state fMRI signal. In this study, fMRI signals in five functional brain networks (sensorimotor, 'default mode', visual, amygdala, and hippocampus) were decomposed into various frequency bands within a low-frequency range (0-0.24 Hz). Results show that the correlations in cortical networks concentrate within ultra-low frequencies (0.01-0.06 Hz) while connections within limbic networks distribute over a wider frequency range (0.01-0.14 Hz), suggesting distinct frequency-specific features in the resting-state fMRI signal within these functional networks. Moreover, the connectivity decay rates along the frequency bands are positively correlated with the physical distances between connected brain regions and seed points. This distance-frequency relationship might be attributed to a larger attenuation of synchrony of brain regions separated with longer distance and/or connected with more synaptic steps.