With searchable encryptions in the cloud computing, users can outsource their sensitive data in ciphertext to the cloud that provides efficient and privacy-preserving multi-keyword top-k searches. However, most existing top-k search schemes over encrypted cloud data are the centralize schemes which are limited in large scale data environment. To support scalable searches, we propose a parallel multi-keyword top-k search scheme over encrypted cloud data. In this scheme, the fragment-based encrypted inverted index is designed, which is indistinguishable and can be used for parallel searching. On the basis of such indexes, a Map-Reduce-based distributed computing framework is adopted to implement the parallel multi-keyword top-k search algorithms. Security analysis and experiment evaluation show that the proposed scheme is privacy-preserving, efficient and scalable.