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McEliece public-key encryption scheme is believed to be an alternative cryptographic scheme, with potential to resist future quantum computers attacks. However, the homomorphism of McEliece public-key cryptographic scheme has not been studied. The technology of homomorphic encryption can operate ciphertext directly and the result of the operation can be automatically encrypted, so it has been widely used. We point out and prove the homomorphism properties of McEliece public-key encryption scheme including additive and mixed homomorphism. We also discuss the application of homomorphism on anonymous vote, function construction and millionaires' problem. The security of homomorphism properties is based on McEliece public-key cryptosystem. The user can complete operations without leaking private information, and the data protection and privacy issues of user can be solved.