Named Data Networking (NDN) is a promising network architecture that differs from the traditional TCP/IP network, as it focuses on data rather than the host. A new secure model is required to provide the data-oriented trust instead of the host-oriented trust. This paper proposes a new secure solution in the NDNs named Secure Mechanism supported by Certificateless Digital Signature and Blockchain (CLDS-B). The CLDS-B scheme employs a certificateless digital signature to guarantee the authentication and integrity of data. On the one hand, the key escrow problem has been solved to eliminate the risks of compromised private key generators; on the other hand, the data name has been bound to the public key to prevent the false public key. Moreover, the blockchain is used to manage cryptographic information. Each domain designates an information service entity to join the blockchain so that the consumer could retrieve the cryptographic information public parameter in the local domain if necessary. Furthermore, due to the decentralization of the blockchain, the CLDS-B would be robust to resist the single-node failure. Simulation results show that the CLDS-B scheme outperforms a classic NDN scheme, although it shows slightly inferior to the other secure NDN scheme. The security verification and analysis show that the CLDS-B would resist the key escrow attack. The CLDS-B would be a competitive solution in scenarios with a high-security level.