Opportunistic routing (OR) is an effective way to guarantee transmission reliability in wireless multi-hop networks. However, little research focuses on transmission efficiency. Thus, an analytical model based on open queuing network with Markov chains was proposed to evaluate the efficiency. By analyzing two typical ORs, we find duplicate transmission and collision avoidance overhead are the root reasons behind inefficiency. Therefore, a new scheme called dual priority cooperative opportunistic routing (DPCOR) was proposed. In DPCOR, forwarding candidates are configured with dual priority, which enables the network to classify forwarding candidates more effectively so as to reduce the back-off time and obtain more diversity gain. Theoretical analysis and simulation results show DPCOR achieves significant performance improvement with less time overhead compared with traditional routings and typical ORs.