Studies have shown that attention bias can affect behavioral indicators in patients with depression, but it is still unclear how this bias affects the brain network topology of patients with mild depression (MD). Therefore, a novel functional brain network analysis and hierarchical clustering methods were used to explore the abnormal brain topology of MD patients based on EEG signals during the visual search paradigm. The behavior results showed that the reaction time of MD group was significantly higher than that of normal group. The results of functional brain network indicated significant differences in functional connections between the two groups, the amount of inter-hemispheric long-distance connections are much larger than intra-hemispheric short-distance connections. Patients with MD showed significantly lower local efficiency and clustering coefficient, destroyed community structure of frontal lobe and parietal-occipital lobe, frontal asymmetry, especially in beta band. In addition, the average value of long-distance connections between left frontal and right parietal-occipital lobes presented significant correlation with depressive symptoms. Our results suggested that MD patients achieved long-distance connections between the frontal and parietal-occipital regions by sacrificing the connections within the regions, which might provide new insights into the abnormal cognitive processing mechanism of depression.