With the growing popularity of cloud computing in recent years, data owners (DOs) now prefer to outsource their data to cloud servers and allow the specific data users (DUs) to retrieve the data. Searchable encryption is an important tool to provide secure search over the encrypted cloud data without infringing data confidentiality and data privacy. In this work, we consider a secure search service providing fine-grained and search functionality, called attribute-based multiple keyword search (ABMKS), which can be seen as an extension of searchable encryption. In the existing ABMKS schemes, the computation operations in the encrypted keyword index generation are time-consuming modular exponentiation, and the number of which is linearly growing with the factor $m$. Here $m$ is the number of keywords embedded in a file. To reduce the computation overhead, in this paper, we propose an ABMKS with only multiplication operations in encrypted keyword index generation. As a result, the computation cost of the encrypted keyword index generation is more efficient than the existing schemes. In addition, the encrypted keyword indexes are aggregated into one item, which is regardless of the number of underlying keywords in a file data. Finally, the security and the performance analysis demonstrate that our scheme is both efficient and secure.