Cloud computing has been regarded as a successful paradigm for IT industry by providing benefits for both service providers and customers. In spite of the advantages, cloud computing also suffers from distinct challenges, and one of them is the inefficient resource provisioning for dynamic workloads. Accurate workload predictions for cloud computing can support efficient resource provisioning and avoid resource wastage. However, due to the high-dimensional and high-variable features of cloud workloads, it is difficult to predict the workloads effectively and accurately. The current dominant work for cloud workload prediction is based on regression approaches or recurrent neural networks, which fail to capture the long-term variance of workloads. To address the challenges and overcome the limitations of existing works, we proposed an efficient supervised learning-based Deep Neural Network (esDNN) approach for cloud workload prediction. First, we utilize a sliding window to convert the multivariate data into a supervised learning time series that allows deep learning for processing. Then, we apply a revised Gated Recurrent Unit (GRU) to achieve accurate prediction. To show the effectiveness of esDNN, we also conduct comprehensive experiments based on realistic traces derived from Alibaba and Google cloud data centers. The experimental results demonstrate that esDNN can accurately and efficiently predict cloud workloads. Compared with the state-of-the-art baselines, esDNN can reduce the mean square errors significantly, e.g., 15%. rather than the approach using GRU only. We also apply esDNN for machines auto-scaling, which illustrates that esDNN can reduce the number of active hosts efficiently, thus the costs of service providers can be optimized.