In this paper, we present an efficient distributed differential quasi-orthogonal space-time block code (DD-QOSTBC) system for multiple relay networks. First, we propose the DD-QOSTBC transmission which considers two robust STBC-like subsystems in amplify-and-forward multiple relaying over flat fading channel. It is assumed that source has two antennas, and relays and destination have a single antenna. With robust STBC-like subsystem structure, we show that our robust subsystems can be used for an efficient joint suboptimal differential decoding based on a maximum likelihood criterion. Finally, we accomplish the performance evaluation on the proposed DD-QOSTBC system in terms of bit-error-rate.