To analyze the time effect of passive pile deformation under the action of surcharge load， this paper first introduces the fractional-order Merchant model to describe the creep characteristics of the soil. Then， based on the correspondence principle and Laplace transform， the Boussinesq viscoelastic solution is derived to calculate the additional horizontal stress induced by the load. The Terzaghi arching model is used to transfer the additional stress to the pile， obtaining the passive load on the pile due to the action of the load. Next， the pile is simplified as an Euler beam on a viscoelastic Pasternak foundation， and the differential equation calculating the deflection of the pile is established. The finite difference method and Laplace inverse transform are used to solve the equation. Subsequently， by comparing the results with existing experimental data， the feasibility of the method proposed in this paper is validated. Finally， the effects of fractional-order Merchant model parameters （elastic modulus Eh of Hooke body， elastic modulus Ek of Kelvin body， viscosity coefficient η， and fractional-order order α）， surcharge load-pile horizontal distance， and surcharge load on pile horizontal displacement are analyzed. The analysis results show that the larger Eh is， the smaller the initial pile horizontal displacement is. The greater Ek is， the smaller the increment of pile horizontal displacement with time， and the greater η results in the longer time for the pile to reach the final deformation. The larger α is， the greater the viscosity of Kelvin body is. The smaller surcharge load-pile horizontal distance and larger load lead to larger horizontal displacement of piles. With increasing time， the sensitivity of pile horizontal displacement to Eh decreases， and the sensitivity of surcharge load-pile horizontal distance and surcharge load increases.