A novel method for predicting the load-settlement response of a single pile in sands is developed based on an interface constitutive model. Firstly, a rigorous nonlinear load-transfer model for the pile-soil interface is derived from the soil-structure interface constitutive model. This model incorporates the beneficial features of the adopted interface constitutive model and effectively simulates fundamental interface characteristics, such as strain hardening (or softening), normal shear dilation, and stress path dependency occurring at the pile-soil interface. Additionally, a hyperbolic load-transfer model is employed to simulate the nonlinear stress-displacement relationship between the pile tip and soil. The parameters for the aforementioned load-transfer model can be calibrated through experimental interface shear tests and geotechnical experiments. Subsequently, a one-dimensional computational model for analyzing the load-settlement response of a single pile is proposed based on the load transfer method, with numerical solutions obtained using an iterative algorithm. Finally, the theoretical results are compared with reported and independently conducted model pile tests to validate the accuracy of the proposed theoretical approach. The experimental results show a good agreement between the predicted and measured values, demonstrating the method’s excellent capability in predicting the load-settlement response of both displacement and non-displacement piles. This paper presents an analytical framework based on the interface constitutive model for analyzing the load-settlement response of single piles, providing a theoretical reference for optimizing the design of pile foundations in sandy soils under vertical loads.