The load-shedding culvert changes the transmission path of the fill load on the culvert roof, causing the fill load to concentrate on the load shedding blocks, thereby reducing the earth pressure on the culvert roof. However, the soil and compressible material in the load shedding hole will creep with time under long-term fill load, leading to stress redistribution. In order to clarify the variation law of earth pressure and load reduction effect of the load-shedding culvert under the long-term fill load, the model test on rigid foundation was used to explore the load transfer law of the load-shedding culvert during the sand filling construction, and the correctness of the numerical model was verified according to the test results. Then the verified numerical model was conducted to analysis the long-term variation law of earth pressure of the load-shedding culvert by considering three different creeps conditions (i.e., the creep of EPS material in the load shedding hole, the creep of embankment fill, and both creeps). The results show that, on rigid foundation, considering the creep of EPS slab, the earth pressure at the top of the culvert decreases by 25.4% in the 30 years of post-construction compared with that at the end of soil filling, the load reduction effect of the earth pressure at the top of the culvert increases with time, it suggests that the vertical earth pressure coefficient on the culvert top can be taken as 0.45. When considering the fill creep or both creeps, the earth pressure at the top of the culvert fluctuates and finally approaches to the self-weight pressure of the fill soil, the load reduction effect gradually decreases with the increase of time, it suggests that the vertical soil pressure coefficient on the culvert roof can be taken as 1.1. For cohesive soil embankment, if the earth pressure redistribution caused by fill creep is not considered in the engineering design, the load reduction effect of the load-shedding culvert probably be overestimated and resulting in structural damage.