For a long period, automated vehicles (AVs) or vehicle platoons will coexist with human-driven vehicles (HDVs) in heterogeneous traffic flow, where the cut-in maneuver of human drivers can be frequently expected. In this paper, to understand and simulate the driver decisions on whether to continue the cut-in and when to execute the lane-change during the cut-in process, we propose a two-layer prediction-based decision model by integrating a dynamic prediction module, a continuity decision module, and an execution decision module. To our best knowledge, this is the first study to model the driver decision behavior of the cut-in process. Cut-in experiments are conducted to collect the decision and control data of drivers under one- and two-target-vehicle scenarios, which both include sixty sub-scenarios with different initial velocities, accelerations, or positions of the vehicles. We prove the effectiveness of the proposed model in simulating the driver decision behavior of the cut-in process by comparing the experimental and simulation results under various scenarios over different subjects. Besides, we analyze the effects of some model parameters on the model performance to show their ability to represent different driving styles.