In this study, a layered parallel algorithm via fuzzy c-means (FCM) technique, called LP-FCM, is proposed in the framework of Map-Reduce for data clustering problems. The LP-FCM mainly contains three layers. The first layer follows a parallel data partitioning method which is developed to randomly divide the original dataset into several subdatasets. The second layer uses a parallel cluster centers searching method based on Map-Reduce, where the classic FCM algorithm is applied to search the cluster centers for each subdataset in Map phases, and all the centers are gathered to the Reduce phase for the confirmation of the final cluster centers through FCM technique again. The third layer implements a parallel data clustering method based on the final cluster centers. After comparing with some famous classic random initialization sequential clustering algorithms which include K-means, K-medoids, FCM and MinMaxK-means on 20 benchmark datasets, the feasibility in terms of clustering accuracy is evaluated. Furthermore, the clustering time and the parallel performance are also tested on some generated large-scale datasets for the parallelism.