Berson pointed out that the McEliece public-key cryptosystem suffers from two weaknesses: (1) failure to protect any message which is encrypted more than once; and (2) failure to protect any messages which have a known linear relationship with one another. In this paper, we propose some variants of the McEliece scheme to prevent Berson’s attacks. In addition, we also propose some secure and efficient variants of the McEliece scheme in order to improve the information rate. On the other hand, designing a public-key cryptosystem which is theoretically secure has become more and more important since the introduction of notions of public-key encryption security by Bellare, Desai, Pointcheval, and Rogaway. In this paper, we also propose a variant of the McEliece scheme that is non-malleable under the adaptive chosen ciphertext attack.