In order to solve the problem that the horizontal displacement of adjacent pile foundation gradually develops with time under the condition of foundation pit excavation in soft soil foundation, a two-stage method is used for analysis. In the first stage, a three-dimensional fractional Merchant viscoelastic model is introduced to describe the rheological properties of soft soil. Combining with the correspondence principle and the Laplace transformation method the Mindlin time-domain solution of the additional stress is obtained. In the second stage, regarding the pile foundation as Timoshenko beam on the Pasternak foundation, the additional stress is loaded on the pile foundation, and the differential equation of pile foundation deformation is established. On this basis, the time-domain solution of horizontal displacement of the pile foundation considering the shear effect of the pile foundation and the thickness of the pile-soil shear layer is obtained through the finite difference method. The correctness of the proposed method is verified by comparing it with the results of existing literature. Finally, the influencing factors of the three-dimensional fractional Merchant viscoelastic model parameters (shear modulus, volume modulus, viscosity coefficient, fractional order) are analyzed. The results show that the numerical solution can well reflect the development law of horizontal displacement of adjacent pile foundations caused by foundation pit excavation with time.