Time series data generated by continuous glucose monitoring sensors offer unparalleled opportunities for developing data-driven approaches, especially deep learning-based models, in diabetes management. Although these approaches have achieved state-of-the-art performance in various fields such as glucose prediction in type 1 diabetes (T1D), challenges remain in the acquisition of large-scale individual data for personalized modeling due to the elevated cost of clinical trials and data privacy regulations. In this work, we introduce GluGAN, a framework specifically designed for generating personalized glucose time series based on generative adversarial networks (GANs). Employing recurrent neural network (RNN) modules, the proposed framework uses a combination of unsupervised and supervised training to learn temporal dynamics in latent spaces. Aiming to assess the quality of synthetic data, we apply clinical metrics, distance scores, and discriminative and predictive scores computed by post-hoc RNNs in evaluation. Across three clinical datasets with 47 T1D subjects (including one publicly available and two proprietary datasets), GluGAN achieved better performance for all the considered metrics when compared with four baseline GAN models. The performance of data augmentation is evaluated by three machine learning-based glucose predictors. Using the training sets augmented by GluGAN significantly reduced the root mean square error for the predictors over 30 and 60-minute horizons. The results suggest that GluGAN is an effective method in generating high-quality synthetic glucose time series and has the potential to be used for evaluating the effectiveness of automated insulin delivery algorithms and as a digital twin to substitute for pre-clinical trials.