This paper addresses how to construct a RBAC-compatible attribute-based encryption (ABE) for secure cloud storage, which provides a user-friendly and easy-to-manage security mechanism without user intervention. Similar to role hierarchy in RBAC, attribute lattice introduced into ABE is used to define a seniority relation among all values of an attribute, whereby a user holding the senior attribute values acquires permissions of their juniors. Based on these notations, we present a new ABE scheme called Attribute-Based Encryption with Attribute Lattice (ABE-AL) that provides an efficient approach to implement comparison operations between attribute values on a poset derived from attribute lattice. By using bilinear groups of composite order, we propose a practical construction of ABE-AL based on forward and backward derivation functions. Compared with prior solutions, our scheme offers a compact policy representation solution, which can significantly reduce the size of privatekeys and ciphertexts. Furthermore, our solution provides a richer expressive power of access policies to facilitate flexible access control for ABE scheme.