As demand for high fidelity multimedia content has soared, content distribution has emerged as a critical application. Large multimedia files require effective content distribution services such as content distribution networks (CDNs). A recent trend in CDN development is the use of peer-to-peer (P2P) techniques. P2P-based CDNs have several advantages over conventional non-P2P-based CDNs in scalability, fault resilience, and cost-effectiveness. Unfortunately, P2P-based content distribution poses a crucial problem in that update propagation is quite difficult to accomplish. This is because peers cannot obtain a global view of replica locations on the network. There are still several issues in conventional approaches to update propagation. They degrade the scalability, the fault resilience, and the cost-effectiveness of P2P-based content distribution, they also consume the network bandwidth, or take a long time. In this paper, we propose the speculative update, which quickly propagates an update to replicas with less bandwidth consumption in a pure P2P fashion. The speculative update enables a fast update propagation on structured P2P-based CDNs. Each server attempts to determine the directions in which there will be replicas with a high probability and speculatively relays update messages in those directions. Simulation results demonstrate that our mechanism quickly propagates an update to replicas with less bandwidth consumption. The The speculative update completes update propagation as fast as the simple gossipbased update propagation even with up to 69% fewer messages per second. Compared to the convergence-guaranteed random walk, the speculative update completes an update propagation faster by up to 92%.