Excessive loading in soft soils will cause significant displacement of adjacent bridge pile foundations, which is extremely detrimental to the safe service of the bridge. Combined with an actual pier deviation case in soft soil caused by surcharge loads, a material model subroutine considering the time-dependent characteristics of lateral deformation of soft soil was proposed, and a finite element model of surcharge load-pile foundation-bridge pier structure was established to study the time-dependent deviation characteristics of bridge pier-cap-pile foundation structure in soft soil area under surcharge loads and to reveal the lateral-deviation mechanism of the bridge pier-cap-pile foundation structure. In addition, effective and reasonable correction measures were proposed for the site conditions. The results show that with the increase of loading time, the pile response distribution along the depth changed significantly, while the time-dependent lateral deformation of the soft soil caused by the surcharge load caused the lateral additional pressure acting on the pile side to gradually increase, but its distribution range along the depth remained unchanged and was mainly distributed in the depth range of the soft-weak soil layer. Based on the assessment of the ultimate bending moment in the pile sections, the pile foundation studied was still in a safe state, but extra attention should be paid to the bending moment at the location of the connection between the cap and the pile foundation and at the interface between the upper soft layer and the lower harder soil layer. In addition, the proposed corrective measure of unloading+high-pressure rotary pile reinforcement can achieve the expected correction effect.