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The cold-start problem is a long-standing challenge in recommender systems due to the lack of user-item interactions, which significantly hurts the recommendation effect over new users and items. Recently, meta-learning based methods attempt to learn globally shared prior knowledge across all users, which can be rapidly adapted to new users and items with very few interactions. Though with significant performance improvement, the globally shared parameter may lead to local optimum. Besides, they are oblivious to the inherent information and feature interactions existing in the new users and items, which are critical in cold-start scenarios. In this paper, we propose a Task aligned Meta-learning based Augmented Graph (TMAG) to address cold-start recommendation. Specifically, a fine-grained task aligned constructor is proposed to cluster similar users and divide tasks for meta-learning, enabling consistent optimization direction. Besides, an augmented graph neural network with two graph enhanced approaches is designed to alleviate data sparsity and capture the high-order user-item interactions. We validate our approach on three real-world datasets in various cold-start scenarios, showing the superiority of TMAG over state-of-the-art methods for cold-start recommendation.