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Neural processes (NPs) are a promising paradigm to enable skill transfer learning across tasks with the aid of the distribution of functions. The previous NPs employ the empirical risk minimization principle in optimization. However, the fast adaption ability to different tasks can vary widely, and the worst fast adaptation can be catastrophic in risk-sensitive tasks. To achieve robust neural processes modeling, we consider the problem of training models in a risk-averse manner, which can control the worst fast adaption cases at a certain probabilistic level. By transferring the risk minimization problem to a two-level finite sum minimax optimization problem, we can easily solve it via a double-looped stochastic mirror prox algorithm with a task-aware variance reduction mechanism via sampling samples across all tasks. The mirror prox technique ensures better handling of complex constraint sets and non-Euclidean geometries, making the optimization adaptable to various tasks. The final solution, by aggregating prox points with the adaptive learning rates, enables a stable and high-quality output. The proposed learning strategy can work with various NPs flexibly and achieves less biased approximation with a theoretical guarantee. To illustrate the superiority of the proposed model, we perform experiments on both synthetic and real-world data, and the results demonstrate that our approach not only helps to achieve more accurate performance but also improves model robustness.