Warehouse accidents have become of wide concern to the public because they often cause heavy economic losses and heavy casualties. Therefore, it is critical to foster the safety and reliability of warehouse facilities to reduce accidents. However, in the relevant literature, the increased safety of warehouse facilities has seldom been researched. This is a main research gap that the authors would like to supplement with the aim of enhancing warehouse facility reliability to improve risk management in a comprehensive and reliable way. The objectives of this research article are to collect the critical risks from the relevant literature and interviewees, to calculate the weights of four critical indicators (O, S, D, and E) by the BWM approach, and to rank the critical risks of picking and material-handling accidents in a warehouse facility through GRA, the HFACS model, and the FMEA approach. The ranking results show that cost is the most essential element and the expected cost > detection > severity > occurrence, according to the average value of experts’ comprehensive consideration of importance. Next, GRA is used to prioritize the critical risks of picking and material-handling accidents. The main contribution is that we identify 18 major critical risk accidents of the HFACS risk categories and make up for the insufficiency of past research that lacks an empirical analysis of the risks of picking and material-handling accidents in warehouse facilities.