A large number of solid particles and fibrous impurities are always entrained in the fluid transported by a sewage pump, which can easily lead to the blockage of the sewage pump. In view of this, CFD–DEM simulations were conducted in this paper to reveal the fiber clogging mechanism in the sewage pump. A CFD–DEM coupling method with a fiber model was established and verified by an experimental benchmark, i.e., the rectangular flow channel. The method was then applied to a model sewage pump to, after mesh independence tests, analyze the effects of flow rate and fiber length on fiber motion and clogging. The results showed that the position of fiber retention coincides with the position of the vortex, mainly located at the inlet of the impeller, the head of the blade, the middle of the blade, and the tongue in the pump. In the case of a low flow rate, the fiber was more likely to cause blockage in the head of the blade, and in the case of a large flow rate, the fiber would wind around the tongue in the pump. At the same flow rate, long fiber was more likely to stay on the blade’s suction surface.