In few-shot learning scenarios, the challenge is to generalize and perform well on new unseen examples when only very few labeled examples are available for each task. Model-agnostic meta-learning (MAML) has gained the popularity as one of the representative few-shot learning methods for its flexibility and applicability to diverse problems. However, MAML and its variants often resort to a simple loss function without any auxiliary loss function or regularization terms that can help achieve better generalization. The problem lies in that each application and task may require different auxiliary loss function, especially when tasks are diverse and distinct. Instead of attempting to hand-design an auxiliary loss function for each application and task, we introduce a new meta-learning framework with a loss function that adapts to each task. Our proposed framework, named Meta-Learning with Task-Adaptive Loss Function (MeTAL), demonstrates the effectiveness and the flexibility across various domains, such as few-shot classification and few-shot regression.