With the continuous emergence of new communication technologies and networking facilities, especially the rapid evolution of mobile networks for 5G and beyond, the requirements for smarter, more reliable, and more efficient mobile network services have been raised. To meet these increasingly challenging requirements, proactive and effective allocation of mobile network resources becomes essential. Accurate mobile traffic prediction is an indispensable component of intelligent and automated network management for developing reliable and sustainable future communication systems. To achieve this, a promising solution is to introduce and utilise artificial intelligence methods such as deep learning to implement highly effective and efficient mobile traffic prediction models. However, there are still some critical challenging issues that need to be solved. For example, the insufficiency of training data hinders obtaining a robust and accurate mobile traffic prediction model, how to improve the prediction performance by jointly exploring the spatial and temporal characteristics of the mobile traffic data, and traditional centralised training of prediction model poses a privacy leakage threat due to the collection of vast amounts of raw data. Moreover, the ever-increasing requirements of service quality have demanded highly accurate mobile traffic prediction. To address these challenges, this thesis aims to investigate and develop accurate mobile traffic prediction by further solving these challenges through advanced deep learning methods. To alleviate the insufficiency of training data, a data augmentation based mobile cellular traffic prediction model (ctGAN-S2S) is proposed, where an effective data augmentation sub-model based on generative adversarial networks is proposed to improve the prediction performance while protecting data privacy, and a long short-term memory based sequence- to-sequence sub-model is used to achieve the flexible multi-step mobile cellular traffic prediction. To explore the spatial and temporal characteristics of the mobile cellular traffic data, a comprehensive investigation and spatial-temporal analysis of mobile cellular network traffic are conducted based on a real-world mobile cellular network traffic dataset. Based on this, a time-series similarity-based graph attention network (TSGAN) for spatial-temporal mobile cellular traffic prediction is proposed. To further improve privacy protection and reduce data leakage risks, a novel federated graph convolutional network model (FGCN) is proposed for secure and accurate spatial-temporal mobile cellular traffic prediction. Extensive experiments are conducted based on real-world cellular network traffic datasets. The results demonstrate that the above proposed deep learning models consistently outperform both the traditional and the state-of-the-art research in wireless communication scenarios.