Generative Adversarial Networks (GAN) have been widely investigated for image synthesis based on their powerful representation learning ability. In this work, we explore the StyleGAN and its application of synthetic food image generation. Despite the impressive performance of GAN for natural image generation, food images suffer from high intra-class diversity and inter-class similarity, resulting in overfitting and visual artifacts for synthetic images. Therefore, we aim to explore the capability and improve the performance of GAN methods for food image generation. Specifically, we first choose StyleGAN3 as the baseline method to generate synthetic food images and analyze the performance. Then, we identify two issues that can cause performance degradation on food images during the training phase: (1) inter-class feature entanglement during multi-food classes training and (2) loss of high-resolution detail during image downsampling. To address both issues, we propose to train one food category at a time to avoid feature entanglement and leverage image patches cropped from high-resolution datasets to retain fine details. We evaluate our method on the Food-101 dataset and show improved quality of generated synthetic food images compared with the baseline. Finally, we demonstrate the great potential of improving the performance of downstream tasks, such as food image classification by including high-quality synthetic training samples in the data augmentation.