The identification of visual attention is an essential part of analyzing the user's visual perception behavior. In this paper, a novel measurement of the center in the fixation cluster based on random walks is developed. In the proposed method, we generate the cluster which includes fixations for a particular region-of-interest (ROI). We form a distance matrix by calculating the point-to-point distances in each cluster and discover the center of the fixation cluster utilizing random walks. Based on the obtained distance matrix, the matrix referring to their transition probability among each other is thereafter constituted. The density of the points in the cluster is also calculated. We utilize the density as the initial coefficient for each fixation and update the coefficients with the consideration of their transition probability and distribution in the cluster. Finally, the generated convergent coefficients are used to weight the fixations and produce the position of the center based on their weighted average. Experimental results demonstrate that the center of the fixation cluster produced by the proposed method outperforms the traditional mean position based method and describes the feature of the viewer's visual attention more accurately.