Data prefetching is an effective way to accelerate data access in high-end computing systems and to bridge the increasing performance gap between processor and memory. In recent years, the contextbased data prefetching has received intensive attention because of its general applicability. In this study, we provide a preliminary analysis of the impact of orders on the effectiveness of the context-based prefetching. Motivated by the observations from the analytical results, we propose a new context-based prefetching method named Multi-Order Context-based (MOC) prefetching to adopt multi-order context analysis to increase the context-based prefetching effectiveness. We have carried out simulation testing with the SPECCPU2006 benchmarks via an enhanced CMP$im simulator. The simulation results show that the proposed MOC prefetching method outperforms the existing single-order prefetching and reduces the data-access latency effectively.