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This paper introduces a new capability of the group signature, called message-dependent opening. It is intended to weaken the higher trust put on an opener, that is, no anonymity against an opener is provided by ordinary group signature. In a group signature system with message-dependent opening (GS-MDO), in addition to the opener, we set up the admitter which is not able to open any user's identity but admits the opener to open signatures by specifying messages whose signatures should be opened. For any signature whose corresponding message is not specified by the admitter, the opener cannot extract the signer's identity from it. In this paper, we present formal definitions and constructions of GS-MDO. Furthermore, we also show that GS-MDO implies identity-based encryption, and thus for designing a GS-MDO scheme, identity-based encryption is crucial. Actually, we propose a generic construction of GS-MDO from identity-based encryption and adaptive NIZK proofs, and its specific instantiation from the Groth-Sahai proof system by constructing a new (k-resilient) identity-based encryption scheme which is compatible to the Groth-Sahai proof.