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Phase synchronization serves as an effective method for analyzing the synchronization of electroencephalogram (EEG) signals among brain regions and the dynamic changes of the brain. The purpose of this paper is to study the construction of the functional brain network (FBN) based on phase synchronization, with a special focus on neural processes related to human balance regulation. This paper designed four balance paradigms of different difficulty by blocking vision or proprioception and collected 19-channel EEG signals. Firstly, the EEG sequences are segmented by sliding windows. The phase-locking value (PLV) of core node pairs serves as the phase-screening index to extract the valid data segments, which are recombined into new EEG sequences. Subsequently, the multichannel weighted phase lag index (wPLI) is calculated based on the new EEG sequences to construct the FBN. The experimental results show that due to the randomness of the time points of body balance adjustment, the degree of phase synchronization of the datasets screened by PLV is more obvious, improving the effective information expression of the subsequent EEG data segments. The FBN topological structures of the wPLI show that the connectivity of various brain regions changes structurally as the difficulty of human balance tasks increases. The frontal lobe area is the core brain region for information integration. When vision or proprioception is obstructed, the EEG synchronization level of the corresponding occipital lobe area or central area decreases. The synchronization level of the frontal lobe area increases, which strengthens the synergistic effect among the brain regions and compensates for the imbalanced response caused by the lack of sensory information. These results show the brain regional characteristics of the process of human balance regulation under different balance paradigms, providing new insights into endogenous neural mechanisms of standing balance and methods of constructing brain networks.