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In video streaming services, predicting the continuous user's quality of experience (QoE) plays a crucial role in delivering high quality streaming contents to the user. However, the complexity caused by the temporal dependencies in QoE data and the non-linear relationships among QoE influence factors has introduced challenges to continuous QoE prediction. To deal with that, existing studies have utilized the Long Short-Term Memory model (LSTM) to effectively capture such complex dependencies, resulting in excellent QoE prediction accuracy. However, the high computational complexity of LSTM, caused by the sequential processing characteristic in its architecture, raises a serious question about its performance on devices with limited computational power. Meanwhile, Temporal Convolutional Network (TCN), a variation of convolutional neural networks, has recently been proposed for sequence modeling tasks (e.g., speech enhancement), providing a superior prediction performance over baseline methods including LSTM in terms of prediction accuracy and computational complexity. Being inspired of that, in this paper, an improved TCN-based model, namely CNN-QoE, is proposed for continuously predicting the QoE, which poses characteristics of sequential data. The proposed model leverages the advantages of TCN to overcome the computational complexity drawbacks of LSTM-based QoE models, while at the same time introducing the improvements to its architecture to improve QoE prediction accuracy. Based on a comprehensive evaluation, we demonstrate that the proposed CNN-QoE model can reach the state-of-the-art performance on both personal computers and mobile devices, outperforming the existing approaches.