We use fuzzy finite element method (FEM) to analyze the impact of cold wave on face slab cracking of a concrete-faced rockfill dam (CFRD). The static response of dam and the temperature field of face slab are calculated using deterministic FEM since some observed and test data can be obtained. Some parameters of Goodman contact element between face slabs and cushion material are selected as fuzzy variables, and the fuzzy FEM is used to calculate fuzzy stress of face slab. The fuzzy FEM is implemented using vertex method based on the extension principle. Through the analysis of two selected calculation cases of cold wave, it is shown that the calculated cracking direction and cracking zone caused by thermal stress are similar to those of the observed cracks. This proves that the cold wave that caused swift air temperature drop is an important reason for the cracking of face slab. According to these analysis results, some cracking prevention measures are then proposed.