The aim of this paper is to present a mobile agents model for distributed classification of Big Data. The great challenge is to optimize the communication costs between the processing elements (PEs) in the parallel and distributed computational models by the way to ensure the scalability and the efficiency of this method. Additionally, the proposed distributed method integrates a new communication mechanism to ensure HPC (High Performance Computing) of parallel programs as distributed one, by means of cooperative mobile agents team that uses its asynchronous communication ability to achieve that. This mobile agents team implements the distributed method of the Fuzzy C-Means Algorithm (DFCM) and performs the Big Data classification in the distributed system. The paper shows the proposed scheme and its assigned DFCM algorithm and presents some experimental results that illustrate the scalability and the efficiency of this distributed method.