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Nowadays, frequent pattern mining (FPM) on large graphs receives increasing attention, since it is crucial to a variety of applications, e.g., social analysis. Informally, the FPM problem is defined as finding all the patterns in a large graph with frequency above a user-defined threshold. However, this problem is nontrivial due to the unaffordable computational and space costs in the mining process. In light of this, we propose a cost-effective approach to mining near-optimal top-k patterns. Our approach applies a "level-wise" strategy to incrementally detect frequent patterns, hence is able to terminate as soon as top-k patterns are discovered. Moreover, we develop a technique to compute the lower bound of support with smart traverse strategy and compact data structures. Extensive experimental studies on real-life and synthetic graphs show that our approach performs well, i.e., it outperforms traditional counterparts in efficiency, memory footprint, recall and scalability.