We investigated why movement of the human eye enables us to swiftly find a target symbol out of many alternatives. To this end, we obtained experimental gaze step data, defined as the distance between two serial gaze positions, on a monitor screen. The frequency distribution of this data approximately follows a power-law distribution. Using this frequency distribution, we constructed a network model to replicate the gaze step dynamics, in which the vertices (or nodes) and the paths between two vertices correspond to the gaze positions (tremors or drifts) and the gaze steps (saccades), respectively. The constructed network has the features of a small-world network. We suggest, therefore, that there is a physiological mechanism in visual search, which reduces the size of the physically wide search area. Such eye movement can find the target symbol in a relatively short time proportional to the logarithm of the number of symbols on the screen.