Awareness of the importance of U-shaped assembly line balancing problems is all on the rise. In the U-shaped assembly line, balancing is affected by the uncertainty associated with the assembly task times. Therefore, it is crucial to develop an approach to respond to the uncertainty caused by the task times. When the great majority of existing literature related to uncertainty in the assembly line is considered, it is observed that the U-shaped assembly line balancing problem under uncertainty is scarcely investigated. That being the case, we aim to fill this research gap by proposing a robust counterpart formulation for the addressed problem. In this study, a robust optimization model is developed for the U-shaped assembly line worker assignment and balancing problem (UALWABP) to cope with the task time uncertainty characterized by a combined interval and polyhedral uncertainty set. A real case study is conducted through data from a company producing water meters.