In massive multiple-input multiple-output (MIMO) systems, how to reliably acquire downlink channel state information (CSI) with low overhead is challenging. In this work, by integrating the generative pre-trained Transformer (GPT) with federated-tuning, we propose a CSI-GPT approach to realize efficient downlink CSI acquisition. Specifically, we first propose a Swin Transformer-based channel acquisition network (SWTCAN) to acquire downlink CSI, where pilot signals, downlink channel estimation, and uplink CSI feedback are jointly designed. Furthermore, to solve the problem of insufficient training data, we propose a variational auto-encoder-based channel sample generator (VAE-CSG), which can generate sufficient CSI samples based on a limited number of high-quality CSI data obtained from the current cell. The CSI dataset generated from VAE-CSG will be used for pre-training SWTCAN. To fine-tune the pre-trained SWTCAN for improved performance, we propose an online federated-tuning method, where only a small amount of SWTCAN parameters are unfrozen and updated using over-the-air computation, avoiding the high communication overhead caused by aggregating the complete CSI samples from user equipment (UEs) to the BS for centralized fine-tuning. Simulation results verify the advantages of the proposed SWTCAN and the communication efficiency of the proposed federated-tuning method.