Computing servers have played a key role in developing and processing emerging compute-intensive applications in recent years. Consolidating multiple virtual machines (VMs) inside one server to run various applications introduces severe competence for limited resources among VMs. Many techniques such as VM scheduling and resource provisioning are proposed to maximize the cost-efficiency of the computing servers while alleviating the performance inference between VMs. However, these management techniques require accurate performance prediction of the application running inside the VM, which is challenging to get in the public cloud due to the black-box nature of the VMs. From this perspective, this paper proposes a novel machine learning-based performance prediction approach for applications running in the cloud. To achieve high accuracy predictions for black-box VMs, the proposed method first identifies the running application inside the virtual machine. It then selects highly-correlated runtime metrics as the input of the machine learning approach to accurately predict the performance level of the cloud application. Experimental results with state-of-the-art cloud benchmarks demonstrate that our proposed method outperforms the existing prediction methods by more than 2x in terms of worst prediction error. In addition, we successfully tackle the challenge in performance prediction for applications with variable workloads by introducing the performance degradation index, which other comparison methods fail to consider. The workflow versatility of the proposed approach has been verified with different modern servers and VM configurations.