To meet the requirements of big data processing, this paper presents an efficient mapping scheme for a fully connected multilayered neural network, which is trained by using back-propagation (BP) algorithm based on MapReduce of cloud computing clusters. The batch-training (or epoch-training) regimes are used by effective segmentation of samples on the clusters, and are adopted in the separated training method, weight summary to achieve convergence by iterating. For a parallel BP algorithm on the clusters and a serial BP algorithm on an uniprocessor, the required time for implementing the algorithms is derived. The performance parameters, such as speedup, optimal number and minimum of data nodes are evaluated for the parallel BP algorithm on the clusters. Experiment results demonstrate that the proposed parallel BP algorithm in this paper has better speedup, faster convergence rate, less iterations than that of the existed algorithms.