We study a finite horizon stochastic inventory routing problem. The supplier acts as a central planner who determines the replenishment quantities as well as the times and routes to all retailers. We allow ambiguity in the probability distribution of uncertain demand of each retailer. We consider from a service-level point of view and minimize the risk of the uncertain inventory levels in violating the pre-specified range. To quantify this risk, we propose a decision criterion, which takes into account both the frequency and magnitudes of violation of the inventory requirement. The solutions are fully-adaptable at each period and vary with the realizations of uncertain demand. We provide algorithms to solve the problem exactly and compare the performance of our solutions with several benchmarks to show their benefits.