The capacitated arc routing problem with time window has been studied for years, while uncertainties in real-world scenarios, such as uncertain demands and uncertain routing conditions, were rarely considered. In this paper, we formulate an uncertain capacitated arc routing problem with time window that takes into account the uncertain demand of tasks, the uncertain deadheading costs and the uncertain presence of tasks and paths. A number of problem instances are generated based on the benchmark instances of static capacitated arc routing problem with time window considering the aforementioned four uncertain factors. To tackle this new challenging problem, we adapt a state-of-the-art algorithm for solving uncertain capacitated arc routing problem, an estimation of distribution algorithm (EDA) with a stochastic local search, to find robust solutions. Another algorithm, a memetic algorithm with extended neighborhood search, is also adapted as a baseline solution algorithm to this challenging problems. Our experimental results indicate that our EDA-based algorithm is effective in finding robust solutions to uncertain capacitated arc routing problems with time window.