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In large-scale e-commerce live-stream recommendation, streamers are classified into different levels based on their popularity and other metrics for marketing. Several top streamers at the head level occupy a considerable amount of exposure, resulting in an unbalanced data distribution. A unified model for all levels without consideration of imbalance issue can be biased towards head streamers and neglect the conflicts between levels. The lack of inter-level streamer correlations and intra-level streamer characteristics modeling imposes obstacles to estimating the user behaviors. To tackle these challenges, we propose a curriculum multi-level learning framework for imbalanced recommendation. We separate model parameters into shared and level-specific ones to explore the generality among all levels and discrepancy for each level respectively. The level-aware gradient descent and a curriculum sampling scheduler are designed to capture the de-biased commonalities from all levels as the shared parameters. During the specific parameters training, the hardness-aware learning rate and an adaptor are proposed to dynamically balance the training process. Finally, shared and specific parameters are combined to be the final model weights and learned in a cooperative training framework. Extensive experiments on a live-stream production dataset demonstrate the superiority of the proposed framework.