Larger deep learning models usually lead to higher model quality with an ever-increasing GPU memory footprint. Although tensor checkpointing techniques have been proposed to enable training under a restricted GPU memory budget, the input tensor dynamics have been unexploited for optimizing performance while reducing GPU memory footprint. Specifically, due to the diverse datasets and subsequent data argumentation, the input tensor size per mini-batch is dynamic during the training process, leading to a changing GPU memory footprint. However, to leverage such input tensor dynamics in checkpointing, there are two challenges to be solved. First, the checkpointing plan needs to be determined during runtime due to the dynamics of input tensors. Second, the checkpointing plan needs to be applied on the fly without significantly deteriorating the performance. In this paper, we propose Mimose, an input-aware tensor checkpointing planner respecting the memory budget while enabling efficient model training on GPU. Mimose builds a lightweight but accurate prediction model of GPU memory usage online, without pre-analyzing the model. It generates a tensor checkpointing plan based on per-layer memory prediction and applies it to training progress on the fly. It also adopts a caching strategy to avoid having to regenerate the plan for repeated input size. Our experiments show that Mimose achieves superior training throughput compared to state-of-the-art memory planners under the same GPU memory budgets.