To learn a good distance metric without any class label information, an algorithm named HDDI-FCM (double indices fuzzy C-means with hybrid distance) is proposed in this paper. In detail, the unknown distance metric is firstly represented as the linear combination of several known distance metrics. Then the algorithm is executed to perform the clustering task as well as learn the most suitable metric simultaneously. To guarantee the convergence of the algorithm, the Steffensen iteration is introduced into the process of updating cluster centers. The selection of parameter for the algorithm is also discussed. The experimental results on a collection of UCI (University of California, Irvine) datasets demonstrate the effectiveness of the proposed algorithm.