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HDD failure prediction can be used to protect data loss or service interruption by early warning before real failure of HDD, and improve the reliability and security of data center. However, most studies focused on HDD failure prediction as binary classification and ignored the gradual deterioration of HDD while lacking fault diagnosis function. Therefore, this paper proposes a HDD failure prediction method based on AE-LSTM to achieve multi-objective tasks: HDD health status multi-classification, HDD RUL prediction and HDD fault diagnosis. Firstly, the decision tree regression was used to intelligently label HDD health status. Secondly, the robust hidden variables were extracted by AE-LSTM from SMART, fed to RUL model and HDD health status classification model. Finally, the HDD fault diagnosis is implemented by computing the difference between the input and output of AE module. By evaluating RF, LSTM and AE-LSTM algorithms on the Backblaze public dataset, experimental results showed that the effectiveness and advantages of AE-LSTM algorithm in multi-objective HDD failure prediction.