With the rapid growth of data, it is desirable to outsource data on remote storage server. The emergency of cloud computing makes the dream true and more and more sensitive data are being centralized into cloud for sharing. Since the public cloud server cannot be fully trusted in protecting them, encryption is a promising way to keep confidentiality but leads to high communication and computation overhead for some useful data operations. Searchable encryption initiated by Song et al. provides an efficient solution to support for keyword-based search directly on encrypted data. Nevertheless, existing work depends on key sharing among authorized users, which inevitably causes the risks of key exposure and abuse. In this paper, the keyword search over encrypted data with differential privileges is addressed. We provide a novel framework for secure outsourcing and sharing of encrypted data on hybrid cloud. The framework is full-featured: i) it enables authorized users to perform keyword-based search directly on encrypted data without sharing the same private key, ii) it provides two-layered access control to achieve fine-grained sharing of encrypted data. The security analysis shows that the proposed generic construction satisfies the requirements of message privacy and keyword privacy.