Attribute based signature (ABS) scheme is an important cryptographic primitive which provides a powerful way for user to control their privacy. However, the computational and storage cost of ABS is reasonable when the number of users involved in the system is huge. In order to reduce the bandwidth needed to transmit attribute based signatures and the time needed to verify them, we propose attribute based sequential aggregate signature (ABSAS) scheme. The ABSAS scheme allows a set of players to sign the different messages compress into a short signature which can greatly decrease the store space. In this paper, we also formalize ABSAS scheme and prove the security of this scheme in the standard model. The analysis shows that our ABSAS scheme has less signature length and need less verify computation than the traditional ABS which is more appropriate for the actual situation, especially where bandwidth is a bottleneck.