The transient internal flow in high-pressure high-temperature high-production (three-high) gas wells may bring about serious fluid-structure interaction (FSI) between natural gas fluid and tubing string. Then, fatigue failure, wear and leakage of tubing string can easily be caused to threaten the wellbore safety and integrity. However, it is difficult to directly adopt the existing FSI model owing to particularity environment of the three-high gas wells. Based on water hammer, FSI and Timoshenko beam theory, a mathematical model expounding FSI phenomenon of the three-high gas wells is established by Poisson, friction and junction coupling, which considers unsteady friction effect, centrifugal and Coriolis force to make FSI characteristics more consistent with the engineering practice. Then, the improved method of characteristics (MOC) is applied into combination solution of the model. Later, the model and solution method is verified by comparing the results with different reference's ones respectively. On this basis, the effects of shut-in time, well depth position, unsteady friction on FSI characteristics are analyzed and discussed systematically. The calculation results are shown that shut-in time and well depth position have a more significant influence on FSI characteristics in three-high gas wells. In addition, FSI characteristics under action of unsteady friction decay faster, the time of the peak value also is delayed accordingly, and cumulative attenuation and cumulative delayed time of FSI characteristics increases with decrease of shut-in time. The FSI model, solution method proposed in this paper and results can provide theoretical basis and reference for the research on FSI and the formulation of shut-in operation for three-high gas wells, and even for highly deviated or horizontal gas wells.