Meta-learning approaches have been proposed to tackle the few-shot learning problem.Typically, a meta-learner is trained on a variety of tasks in the hopes of being generalizable to new tasks. However, the generalizability on new tasks of a meta-learner could be fragile when it is over-trained on existing tasks during meta-training phase. In other words, the initial model of a meta-learner could be too biased towards existing tasks to adapt to new tasks, especially when only very few examples are available to update the model. To avoid a biased meta-learner and improve its generalizability, we propose a novel paradigm of Task-Agnostic Meta-Learning (TAML) algorithms. Specifically, we present an entropy-based approach that meta-learns an unbiased initial model with the largest uncertainty over the output labels by preventing it from over-performing in classification tasks. Alternatively, a more general inequality-minimization TAML is presented for more ubiquitous scenarios by directly minimizing the inequality of initial losses beyond the classification tasks wherever a suitable loss can be defined.Experiments on benchmarked datasets demonstrate that the proposed approaches outperform compared meta-learning algorithms in both few-shot classification and reinforcement learning tasks.