At present, the fully homomorphic encryption method has disadvantages of large key size and low calculation efficiency, and it is not practical for the secure cloud computing. We develop a hybrid cloud computing scheme based on the Paillier algorithm which is additively homomorphic, and RSA encryption algorithm which is multiplicative homomorphic. Customer's calculation requests can be described as the combination of simple add and multiplicative operation and the operands. An Encryption Decryption Machine which running in the private cloud processes the encryption according to the type of the operation and upload the cipher texts to the public cloud. The public cloud process calculation without knowing the exact data. Then we run simulations and analyze the results, and the results show that the scheme is practical and efficient.