The designated verifier signature only enables the designated verifier to check the correctness of the signature, while any third party can not verify whether this signature is valid or not. Most of the previous designated verifier signature schemes depend on certificate-based cryptography or identity-based cryptography, while little attention has been paid to the certificateless designated verifier signature scheme which has much more advantages than the previous constructions. In this paper, we propose the first certificateless strong designated verifier signature scheme with non-delegatability. We show that our scheme satisfies the basic properties of a designated verifier signature scheme and resists the two types of adversaries in certificateless cryptography. In addition, the comparison with other existing certificateless SDVS schemes demonstrates the proposed scheme is provided with a good level of security and performance.