Non-Interactive Zero-Knowledge (NIZK for short) proofs are fascinating and extremely useful in many security protocols. In this paper, a new group signature scheme, decisional linear assumption group signature (DLAGS for short) with NIZK proofs is proposed which can prove and sign the multiple values rather than individual bits based on DLIN assumption. DLAGS does not need to interact between the verifier and issuer, which can decrease the communication times and storage cost compared with the existing interactive group signature schemes. We prove and sign the blocks of messages instead of limiting the proved message to only one bit (0 or 1) in the conventional non-interactive zero-knowledge proof system, and we also prove that our scheme satisfy the property of anonymity, unlinkability and traceability. Finally, our scheme is compared with the other scheme (Benoitts scheme) which is also based on the NIZK proofs system and the DLIN assumption, and the results show that our scheme requires fewer members of groups and computational times.