In this paper, we propose a multi-signature scheme, in which each signer can express her intention associating with the message to be signed. Signers' intentions mean a kind of information which can be newly attached to a signature in signers' generating it. However, we have never been introduced any multi-signature scheme dealing with intentions without loss of its efficiency. First, we consider a multi-signature scheme realizing the concept of signers' intentions by utilizing existing schemes, and name it primitive method. After that, we introduce the proposed multi-signature scheme which are more efficient in view of the computational cost for verification and in view of the signature size than primitive method. The proposed multi-signature scheme is shown to be secure even against adaptive chosen message insider attacks.