Certificateless signcryption is a useful cryptographic primitive which simultaneously provides the functionalities of certificateless encryption and certificateless signature.In the past few years, some certificateless signcryption schemes have been proposed, and claimed to be provably secure.Unfortunately, concrete attacks can be made that indicate that some existing certificateless signcryption schemes are not secure.To overcome these disadvantages, an efficient certificateless signcryption scheme without bilinear pairings is proposed.The proposal is provably secure in the random oracle model based on the computational Diffie-Hellman problem and discrete logarithm problem, and also has the security properties such as non-repudiation and public verifiability.Additionally, compared with other existing certificateless signcryption schemes in the computational complexity, the proposed method is more efficient and secure due to the lack of bilinear pairings.