The emergence of edge computing makes it possible to realize new technologies such as virtual reality and augmented reality. However, a large number of devices and more messages at the edge bring more security problems. Therefore, it is an important research topic to provide users with faster network services while ensuring confidentiality and authentication of data transmission. Because signcryption can encrypt and sign messages at the same time, it has become a new cryptographic primitive. In the meantime, certificateless signcryption guarantees data confidentiality and authentication and addresses traditional single point failure problems based on the trust center and the problem of relying on a trusted third party. Therefore, certificateless signcryption has attracted great attention from academia and industry. But certificateless signcryption also faces two types of attacks. In order to more effectively resist these two types of attacks, we propose a certificateless signcryption mechanism based on blockchain. This mechanism can make good use of the nontamperable feature of blockchain, prevent illegal users from substituting public key of the user, and guarantee signature non-repudiation. And our scheme is investigated in a comparative study with eight schemes. Comparative analysis outcomes demonstrate our scheme has achieved better results in efficiency and security. The process of signcryption and unsigncryption consumes the least amount of computation, which is very suitable for the edge computing environment.