Certificate-based cryptography is a new cryptographic primitive which eliminates the necessity of certificates in the traditional public key cryptography and simultaneously overcomes the inherent key escrow problem suffered in identity-based cryptography. However, to the best of our knowledge, all existed constructions of certificate-based encryption so far have to be based on the bilinear pairings. The pairing calculation is perceived to be expensive compared with normal operations such as modular exponentiations in finite fields. The costly pairing computation prevents it from wide application, especially for the computation limited wireless sensor networks. In order to improve efficiency, we propose a new certificate-based encryption scheme that does not depend on the pairing computation. Based on the decision Diffie-Hellman problem assumption, the scheme"s security is proved to be against the chosen ciphertext attack in the random oracle. Performance comparisons show that our scheme outperforms the existing schemes.