Data access control has been one of the major challenging issues in cloud computing, especially for sensitive data that have serious privacy concerns about outsourcing to the cloud servers. attribute based encryption is a promising system that provides a fine-grained access control for a distributed system like cloud computing. Yet the existing attribute-based access control (ABAC) approaches suffer from heavy cryptographic computation and communication overhead. In this paper we propose an advanced lightweight attribute-based access control scheme, LABAC, based on elliptic curve integrated encryption scheme ECIES, which provide high-level data confidentiality and data integrity, and has much stronger bit security and shorter length of key , than other exponential-based public key algorithms, combined with KP-ABE known as the best efficient system that ensure fine-grained access control in cloud computing. our scheme ensures fine-grained access control, data confidentiality and provides semantic security against chosen cipher-text attacks than other existing attribute-based access control scheme. The proof security, execution efficiency and performance comparison among LABAC and related ABE scheme are given to prove the execution efficiency and low-cost communication overhead of our scheme LABAC.