Cloud computing services have become indispensable to people’s lives. Many of their activities are performed through cloud services, from small companies to large enterprises and individuals to government agencies. It has enabled clients to use companies’ services on demand at the lowest cost anywhere, anytime, over the Internet. Despite these advantages, cloud networks are vulnerable to many types of attacks. However, as the adoption of cloud services accelerates, the risks associated with these services have also increased. For this reason, solutions have been implemented to improve cloud security, such as monitoring networks, the backbone of the cloud infrastructure, and detecting and classifying cyberattacks. Therefore, an intrusion detection system (IDS) is one of the essential defenses for detecting attacks in the cloud computing network. Current IDSs encounter some challenges in handling and simultaneously analyzing the large scale of traffic found in the cloud environment, and this affects the accuracy of cyberattack detection. Therefore, this research proposes a deep learning-based model by leveraging advanced convolutional neural networks (CNNs)-based model architecture to detect cyberattacks in the cloud environment efficiently. The proposed CNN-based model for intrusion detection consists of multiple significant stages: dataset collection, preprocessing, the SMOTE balance data strategy, feature selection, model training, testing, and performance evaluation. Experiments have demonstrated that the proposed model is highly effective in protecting cloud networks against various potential attacks. With over 98.67% accuracy, precision, and recall, the model has proven its ability to detect and classify network intrusions. Detailed analyses show that the model is proficient in securing cloud security measures and mitigating the risks associated with evolving security threats.