Optimization-based meta-learning typically assumes tasks are sampled from a single distribution - an assumption oversimplifies and limits the diversity of tasks that meta-learning can model. Handling tasks from multiple different distributions is challenging for meta-learning due to a so-called task ambiguity issue. This paper proposes a novel method, ST-MAML, that empowers model-agnostic meta-learning (MAML) to learn from multiple task distributions. ST-MAML encodes tasks using a stochastic neural network module, that summarizes every task with a stochastic representation. The proposed Stochastic Task (ST) strategy allows a meta-model to get tailored for the current task and enables us to learn a distribution of solutions for an ambiguous task. ST-MAML also propagates the task representation to revise the encoding of input variables. Empirically, we demonstrate that ST-MAML matches or outperforms the state-of-the-art on two few-shot image classification tasks, one curve regression benchmark, one image completion problem, and a real-world temperature prediction application. To the best of authors' knowledge, this is the first time optimization-based meta-learning method being applied on a large-scale real-world task.