Spatiotemporal data is prevalent in a wide range of edge devices, such as those used in personal communication and financial transactions. Recent advancements have sparked a growing interest in integrating spatiotemporal analysis with large-scale language models. However, spatiotemporal data often contains sensitive information, making it unsuitable for open third-party access. To address this challenge, we propose a Graph-GAN-based model for generating privacy-protected spatiotemporal data. Our approach incorporates spatial and temporal attention blocks in the discriminator and a spatiotemporal deconvolution structure in the generator. These enhancements enable efficient training under Gaussian noise to achieve differential privacy. Extensive experiments conducted on three real-world spatiotemporal datasets validate the efficacy of our model. Our method provides a privacy guarantee while maintaining the data utility. The prediction model trained on our generated data maintains a competitive performance compared to the model trained on the original data.