Memristors show great promise in neuromorphic computing owing to their high-density integration, fast computing and low-energy consumption. However, the non-ideal update of synaptic weight in memristor devices, including nonlinearity, asymmetry and device variation, still poses challenges to the in-situ learning of memristors, thereby limiting their broad applications. Although the existing offline learning schemes can avoid this problem by transferring the weight optimization process into cloud, it is difficult to adapt to unseen tasks and uncertain environments. Here, we propose a bi-level meta-learning scheme that can alleviate the non-ideal update problem, and achieve fast adaptation and high accuracy, named Rapid One-step Adaption (ROA). By introducing a special regularization constraint and a dynamic learning rate strategy for in-situ learning, the ROA method effectively combines offline pre-training and online rapid one-step adaption. Furthermore, we implemented it on memristor-based neural networks to solve few-shot learning tasks, proving its superiority over the pure offline and online schemes under noisy conditions. This method can solve in-situ learning in non-ideal memristor networks, providing potential applications of on-chip neuromorphic learning and edge computing.