The fuzzy K-modes clustering algorithm is an extension of the fuzzy K-means clustering algorithm, which can handle massive categorical data. However, the quality of the initial cluster centers (or called initial centers) may significantly affect the results of fuzzy K-modes clustering. In many cases, poor clustering results may occur due to unsuitable initial centers. Therefore, the selection of initial centers, that is, cluster center initialization (CCI), is a key issue in fuzzy K-modes clustering. This paper deals with the CCI problem of fuzzy K-modes clustering from the perspective of outlier detection, and proposes a cluster center initialization algorithm (CCI_DOFD), for fuzzy K-modes clustering. CCI_DOFD selects initial centers by virtue of the distance outlier factor of each object, the density of each object and the distances between objects. By considering the distance outlier factor, CCI_DOFD can avoid the problem that an outlier is selected as the initial center. Moreover, when calculating the density of each object and the distances between objects, CCI_DOFD assigns different weights to different attributes according to the significance of each attribute, which can effectively reflect the difference between different attributes. Experimental results on several UCI data sets demonstrate the effectiveness of our algorithm for the CCI of fuzzy K-modes clustering.