With the development of cloud computing,the prediction of trend is important for managing big data.Machine learning classification is an useful tool for predicting trend accurately by analyzing big data.Because traditional public key scheme couldnt support homomorphic operations without decryption,the users data should be encrypted by fully homomorphic encryption (FHE).then they are stored and computed on the cloud server without leaking the users privacy.In this papery we propose an improved fully homomorphic encryption scheme.Gentrys relinearization technique is used to reduce the size of the ciphertext from three ring elements to two ring elements.For practical consideration if there is no homomorphic multiplication for the multiplicative ciphertext.it can be computed homomorphically without using the relinearization technique.In Bosts scheme.private hyperplane decision classification,private Na(i)ve Bayes classification and private decision tree are implemented by partial homomorphic encryption.In order to eliminate too many interactions and ciphertext transformation.we choose proposed FHE scheme.In our homomorphic comparison protocol.the number of interactions between the user and the cloud server is reduced from 3 to 1.The technique of single instruction multiple data (SIMD) is used to speed up homomorphic operations.For efficient implementation of the private decision tree classification,we calculate ciphertexts with the same depth of homomorphic multiplication by the technique of SIMD.Simulation results shows that our implementation of the private decision tree classification is more efficient than Bosts scheme and Khedrs scheme.