The importance of network management is more and more apparent, along with the quick evolution of network technology. Correct network topology is the basis of network management. IPv6 has been recognized as the next generation Internet protocol. However, its large address space and special features bring new challenges for topology discovery. Nowadays, the topology discovery based on ICMP can be divided into distributed method and centralized method, both of which produce the probing redundancy inevitably for probing actively. The distributed topology discovery is difficult to deploy, and its cost is very high. It also has a lot of limitations in redundancy reduction, due to inter-redundancy. Thus, it can't discover topology in a network-friendly manner. Since routers in IPv6 support the source routing function, the centralized topology discovery method can cover the cross link. In this paper, the intra-redundancy generated by one monitor probing is measured, and then a centralized topology discovery method with smallest-redundancy is proposed in IPv6 environment. Based on the backward algorithm, an improved algorithm is presented to reduce redundancy in practical network environment. Meanwhile, the centralized topology discovery method based on source routing in IPv6 is proved feasible. The experiment results show that this method can reduce redundancy of nodes near the monitor by two orders of magnitude, and obtain satisfactory coverage as well.