The frame structure design is more challenging in the new mobile multi-hop relay based (MMR) network architecture, as numerous dimensions of design constraints and challenges have been introduced. Tao et al. propose a simple yet flexible multi-zone framework based upon the current 802.16e OFDMA frame structure design, which enables multi-hop operation while still maintaining the backward compatibility with the legacy mobile stations. However, RS in each tier has different time of receiving data from BS. This time gap is wide and enlarges the ratio of relay zone in frame structure, which decreases system throughput. In addition, this scheme is not considering frequency reuse. In this paper, we propose a MMR frame structure which improves performance while maintaining the backward compatibility. We design the frame structure with frequency reuse. We divide relay zone into several sub relay zones and BS transmits the data starting from the last tier RS to the first tier RS. As a result, we minimize the average time gap of receiving data for RSs. With our proposed frame structure, our simulation shows improvement of MAC efficiency by 30% compared with the scheme by Tao et al.