Neuroimaging studies have demonstrated that the topological properties of resting-state brain functional networks are modulated through task performances. However, the reconfiguration of functional networks associated with distinct degrees of task demands is not well understood. In the present study, we acquired fMRI data from 18 healthy adult volunteers during resting-state (RS) and two visual tasks (i.e., visual stimulus watching, VSW; and visual stimulus decision, VSD). Subsequently, we constructed the functional brain networks associated with these three conditions and analyzed the changes in the topological properties (e.g., network efficiency, wiring-cost, modularity, and robustness) among them. Although the small-world attributes were preserved qualitatively across the functional networks of the three conditions, changes in the topological properties were also observed. Compared with the resting-state, the functional networks associated with the visual tasks exhibited significantly increased network efficiency and wiring-cost, but decreased modularity and network robustness. The changes in the task-related topological properties were modulated according to the task complexity (i.e., from RS to VSW and VSD). Moreover, at the regional level, we observed that the increased nodal efficiencies in the visual and working memory regions were positively associated with the increase in task complexity. Together, these results suggest that the increased efficiency of the functional brain network and higher wiring-cost were observed to afford the demands of visual tasks. These observations provide further insights into the mechanisms underlying the reconfiguration of the brain network during task performance.