In Named-Data Networking (NDN), content is cached in network nodes and served for future requests. This property of NDN allows attackers to inject poisoned content into the network and isolate users from valid content sources. Since a digital signature is embedded in every piece of content in NDN architecture, poisoned content is discarded if routers perform signature verification; however, if every content is verified by every router, it would be overly expensive to do. In our preliminary work, we have suggested a content verification scheme that minimizes unnecessary verification and favors already verified content in the content store, which reduces the verification overhead by as much as 90% without failing to detect every piece of poisoned content. Under this scheme, however, routers are vulnerable to verification attack, in which a large amount of unverified content is accessed to exhaust system resources. In this paper, we carefully look at the possible concerns of our preliminary work, including verification attack, and present a simple but effective solution. The proposed solution mitigates the weakness of our preliminary work and allows this paper to be deployed for real-world applications.