Building models of natural language processing (NLP) is challenging in low-resource scenarios where limited data are available. Optimization-based meta-learning algorithms achieve promising results in low-resource scenarios by adapting a well-generalized model initialization to handle new tasks. Nonetheless, these approaches suffer from the memorization overfitting issue, where the model tends to memorize the meta-training tasks while ignoring support sets when adapting to new tasks. To address this issue, we propose a memory imitation meta-learning (MemIML) method that enhances the model’s reliance on support sets for task adaptation. Specifically, we introduce a task-specific memory module to store support set information and construct an imitation module to force query sets to imitate the behaviors of support sets stored in the memory. A theoretical analysis is provided to prove the effectiveness of our method, and empirical results also demonstrate that our method outperforms competitive baselines on both text classification and generation tasks.