In this paper, we conduct a complex-network analysis of the Bitcoin network. In particular, we design a new sampling method namely random walk with flying-back (RWFB) to conduct effective data sampling. We then conduct a comprehensive analysis of the Bitcoin network in terms of the degree distribution, clustering coefficient, the shortest path length, the assortativity, and the rich-club coefficient. There are several important observations from the Bitcoin network, such as small-world phenomenon and non-rich-club effect. This work brings up an in-depth understanding of the current Bitcoin blockchain network and offers implications for future directions in malicious activity and fraud detection in cryptocurrency blockchain networks.